2024/G9/12: Difference between revisions
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<math>\mathbf{Chapter 3 Section 2}</math><br> | qQ`<math>\mathbf{Chapter 3 Section 2}</math><br> | ||
<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{(2x^4+x^4+x^3+12x+6-[3x^4+3x^2-6x^2]}{(x^3+6)^2}</math><br> | <math>=\frac{(2x^4+x^4+x^3+12x+6-[3x^4+3x^2-6x^2]}{(x^3+6)^2}</math><br> | ||
<math>=\frac{-x^4-2x^3+6x^2+12x+6}{(x^3+6)^2}</math><br> | <math>=\frac{-x^4-2x^3+6x^2+12x+6}{(x^3+6)^2}</math><br> | ||
<math>\mathbf{Ex.5}</math><br> | |||
<math>y=\frac{e^x}{1+x^2}\,(1,\frac{e}{2})\,</math><br> | |||
<math>{\frac{d}{dx}}=\frac{e^x\cdot(1+x^2)-e^x(2x)}{(1+x^2)^2}</math><br> | |||
<math>{\frac{d}{dx}} | |||
Revision as of 15:52, 30 March 2023
qQ`
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 g(4)=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 g^\prime(4)=3}
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^\prime(x)=\frac{1}{2\sqrt{x}}\cdot{g(x)}+\sqrt{x}\cdot{g^\prime(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 \mathbf{Ex.4}}
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=\frac{\color{Blue}{x^2+x-2}}{\color{Red}{x^3+6}}}
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}}=y^\prime=\frac{(2x+1)(x^3-6)-\color{Blue}{(x^2+x-2)}(3x^2)}{\color{Red}{(x^3+6)^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 =\frac{(2x^4+x^4+x^3+12x+6-[3x^4+3x^2-6x^2]}{(x^3+6)^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 =\frac{-x^4-2x^3+6x^2+12x+6}{(x^3+6)^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 \mathbf{Ex.5}}
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=\frac{e^x}{1+x^2}\,(1,\frac{e}{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 {\frac{d}{dx}}=\frac{e^x\cdot(1+x^2)-e^x(2x)}{(1+x^2)^2}}
<math>{\frac{d}{dx}}
![{\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}}[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)
![{\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}}[f\cdot {g}]={\frac {d}{dx}}[f]\cdot {g}+{\frac {d}{dx}}[g]\cdot {f}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/57ee97cfd2a83cef00e5454484f44a5c99a73190)
![{\displaystyle {\frac {d}{dx}}[{\frac {f}{g}}]={\frac {{\frac {d}{dx}}[f]\cdot {g}-{\frac {d}{dx}}[g]\cdot {f}}{g^{2}}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/33117095dc4fc9bab8b77262a36eac752e1beaa5)
