2024/G1/3: Difference between revisions
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==3.3 DERIVATIVE OF TRIGONOMETRIC FUNCTIONS== | ==3.3 DERIVATIVE OF TRIGONOMETRIC FUNCTIONS== | ||
<math> \lim_{ | <math> \lim_{a\to 0} \frac{sin(a)}{0} = 1 </math><br> | ||
<math> \lim_{a\to 0} \frac{cos(a)}{0} = 0 </math><br> | |||
<math> {\frac{d}{dx}} [sin(0)] = cos(0) </math><br> | |||
<math> {\frac{d}{dx}} [cos(0)] = -sin(0) </math><br> | |||
<math> {\frac{d}{dx}} [tan(0)] = sec^2(0) </math><br> | |||
<math> {\frac{d}{dx}} [csc(0)] = csc(0) \cdot cot(0) </math><br> | |||
<math> {\frac{d}{dx}} [sec(0)] = sec(0) \cdot tan(0) </math><br> | |||
<math> {\frac{d}{dx}} [cot(0)] = -csc^2(0) </math><br> | |||
===Ex.2=== | |||
<math> f(x) = \frac{sec(x)}{1+tan(x)} </math><br> | |||
<math> F'(x) = \frac{[sec(x) \cdot tan(x)][1+tan(x)] - sec(x)[sec^2(x)}{[1+tan(x)]^2} </math><br> | |||
<math> F'(x) = \frac{sec(x)[tan(x)+tan^2(x)-sec^2(x)}{[1+tan(x)]^2} </math><br> | |||
<math> F'(x) = \frac{sec(x)(tan(x)+tan^2(x)-tan^2(x)-1)}{[1+tan(x)]^2} </math><br> | |||
<math> F'(x) = \frac{sec(x)[tan(x)-1]}{[1+tan(x)]^2} </math><br> | |||
<math> sec(x) = 0 \qquad tan(x)-1=0 \qquad tan(x)=1 </math> | |||
[[File:62f2b3b7b7b09276a4ad01f2_Unit%20Circle%20Degrees.gif|caption]] | |||
===Ex. 3=== | |||
==3.4 == | ==3.4 == | ||
Latest revision as of 16:42, 25 April 2023
3.1 DERIVATIVE OF POLYNOMIALS AND EXPONENTIAL FUNCTIONS
3.2 THE PRODUCT AND QUOTIENT RULES
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle {\frac{d}{dx}} [c] = 0 }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle {\frac{d}{dx}} [c\cdot f(x)] = c\cdot{\frac{d}{dx}} [f(x)] }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle {\frac{d}{dx}} [f(x)\pm g(x)] = {\frac{d}{dx}} [f(x)] \pm {\frac{d}{dx}} [g(x)] }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle {\frac{d}{dx}} [x^n] = n \cdot x^n-1 }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle {\frac{d}{dx}} [a^x] = \ln(a)a^x }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle {\frac{d}{dx}} [e^x] = e^x }
3.3 DERIVATIVE OF TRIGONOMETRIC FUNCTIONS
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \lim_{a\to 0} \frac{sin(a)}{0} = 1 }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \lim_{a\to 0} \frac{cos(a)}{0} = 0 }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle {\frac{d}{dx}} [sin(0)] = cos(0) }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle {\frac{d}{dx}} [cos(0)] = -sin(0) }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle {\frac{d}{dx}} [tan(0)] = sec^2(0) }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle {\frac{d}{dx}} [csc(0)] = csc(0) \cdot cot(0) }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle {\frac{d}{dx}} [sec(0)] = sec(0) \cdot tan(0) }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle {\frac{d}{dx}} [cot(0)] = -csc^2(0) }
Ex.2
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle f(x) = \frac{sec(x)}{1+tan(x)} }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle F'(x) = \frac{[sec(x) \cdot tan(x)][1+tan(x)] - sec(x)[sec^2(x)}{[1+tan(x)]^2} }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle F'(x) = \frac{sec(x)[tan(x)+tan^2(x)-sec^2(x)}{[1+tan(x)]^2} }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle F'(x) = \frac{sec(x)(tan(x)+tan^2(x)-tan^2(x)-1)}{[1+tan(x)]^2} }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle F'(x) = \frac{sec(x)[tan(x)-1]}{[1+tan(x)]^2} }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle sec(x) = 0 \qquad tan(x)-1=0 \qquad tan(x)=1 }
caption
Ex. 3
3.4
Point Slope Form
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle y - y_1 = m(x - x_1) }