2024/G1/3: Difference between revisions
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(Created page with "==Ch3 Sec2 Review== <math>{\frac{d}{dx}} [c] = 0 </math> <br> <math>{\frac{d}{dx}} [c\cdot f(x)] = c\cdot{\frac{d}{dx}} [f(x)] </math> <br> <math>{\frac{d}{dx}} [f(x)\pm g(x)] = {\frac{d}{dx}} [f(x)] \pm {\frac{d}{dx}} [g(x)] </math> <br> <math> {\frac{d}{dx}} [x^n] = n \cdot x^n-1 </math> <br> <math>{\frac{d}{dx}} [a^x] = \ln(a)a^x </math><br> <math> {\frac{d}{dx}} [e^x] = e^x </math><br> ==Ch3 Sec4 == ===Point Slope Form=== <math> y - y_1 = m(x - x_1) </math> <br>") |
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== | ==3.1 DERIVATIVE OF POLYNOMIALS AND EXPONENTIAL FUNCTIONS== | ||
==3.2 THE PRODUCT AND QUOTIENT RULES== | |||
<math>{\frac{d}{dx}} [c] = 0 </math> <br> | <math>{\frac{d}{dx}} [c] = 0 </math> <br> | ||
<math>{\frac{d}{dx}} [c\cdot f(x)] = c\cdot{\frac{d}{dx}} [f(x)] </math> <br> | <math>{\frac{d}{dx}} [c\cdot f(x)] = c\cdot{\frac{d}{dx}} [f(x)] </math> <br> | ||
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<math> {\frac{d}{dx}} [e^x] = e^x </math><br> | <math> {\frac{d}{dx}} [e^x] = e^x </math><br> | ||
== | ==3.3 DERIVATIVE OF TRIGONOMETRIC FUNCTIONS== | ||
<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 == | |||
===Point Slope Form=== | ===Point Slope Form=== | ||
<math> y - y_1 = m(x - x_1) </math> <br> | <math> y - y_1 = m(x - x_1) </math> <br> | ||
Latest revision as of 16:42, 25 April 2023
3.1 DERIVATIVE OF POLYNOMIALS AND EXPONENTIAL FUNCTIONS
3.2 THE PRODUCT AND QUOTIENT RULES
![{\displaystyle {\frac {d}{dx}}[c]=0}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/834381b512bc1d1fc47c2d26ce38ae71daaa1053)
![{\displaystyle {\frac {d}{dx}}[c\cdot f(x)]=c\cdot {\frac {d}{dx}}[f(x)]}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/e100ac3ba73695d9c36ad8ada81efba4c2a01129)
![{\displaystyle {\frac {d}{dx}}[f(x)\pm g(x)]={\frac {d}{dx}}[f(x)]\pm {\frac {d}{dx}}[g(x)]}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/27fc302c62ab11c846d1255170f40351d3461dfe)
![{\displaystyle {\frac {d}{dx}}[x^{n}]=n\cdot x^{n}-1}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/02df667a9de22b7a499cb1b37b3df322b3bfc5a4)
![{\displaystyle {\frac {d}{dx}}[a^{x}]=\ln(a)a^{x}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/63daf7259a950f7e09db6f16b13e760574c26bf7)
![{\displaystyle {\frac {d}{dx}}[e^{x}]=e^{x}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/783a58bf19ce36ca7781d7d31d78161a55406bff)
3.3 DERIVATIVE OF TRIGONOMETRIC FUNCTIONS
![{\displaystyle {\frac {d}{dx}}[sin(0)]=cos(0)}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/69b11753301c786d83cac2c4b818a62b21cefa89)
![{\displaystyle {\frac {d}{dx}}[cos(0)]=-sin(0)}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/1954b1d317018ba052392032da13755aa2485af6)
![{\displaystyle {\frac {d}{dx}}[tan(0)]=sec^{2}(0)}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/09f1d6ca0893ecac173ba5eb325805414dac785f)
![{\displaystyle {\frac {d}{dx}}[csc(0)]=csc(0)\cdot cot(0)}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/93878095ae2348a74da452932f520bd93ed55f77)
![{\displaystyle {\frac {d}{dx}}[sec(0)]=sec(0)\cdot tan(0)}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/e2bafca0d700c5adcc81f709bd32b63097c836b1)
![{\displaystyle {\frac {d}{dx}}[cot(0)]=-csc^{2}(0)}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/5171a92c94d8fbbcc1793964311cb47c58846022)
Ex.2
![{\displaystyle F'(x)={\frac {[sec(x)\cdot tan(x)][1+tan(x)]-sec(x)[sec^{2}(x)}{[1+tan(x)]^{2}}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/77842aa3b7bf8e3f3085375858c84e39bdff8ffc)
![{\displaystyle F'(x)={\frac {sec(x)[tan(x)+tan^{2}(x)-sec^{2}(x)}{[1+tan(x)]^{2}}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/24295e7c6127b0e10997d437cf16161e1e544e36)
![{\displaystyle F'(x)={\frac {sec(x)(tan(x)+tan^{2}(x)-tan^{2}(x)-1)}{[1+tan(x)]^{2}}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/89b5a7a610e4b23e621cdd9e9d051c6eb27c67f3)
![{\displaystyle F'(x)={\frac {sec(x)[tan(x)-1]}{[1+tan(x)]^{2}}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/89a36dd4ab86c1c18dda783a51a54b543bb1314f)
Ex. 3
3.4
Point Slope Form
