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| ====example 1==== | | ====example 1==== |
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| <math>a'(x)= x^3 {(2x-5)}^4</math> | | <math>f'(x)= x^2 \sqrt[2]{4-9x}</math> |
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| Product Rule <math>(f*g)'=f*g'+ g*f'</math>
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| <math>f=x^3</math>
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| <math>f'=3x^2</math>
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| <math>g={(2x-5)}^4</math>
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| <math>g'=4 {(2x-5)}^3 (2)</math>
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| <math>a' = (x^3)(3x^2) + ({(2x-5)}^4)(4 {(2x-5)}^3 (2))</math>
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| ====example 2==== | | ====example 2==== |
| <math>f'(x)= x^2 \sqrt[2]{4-9x}</math> simplify | | <math>f'(x)= x^2 \sqrt[2]{4-9x}</math> simplify |
Revision as of 14:57, 8 October 2021
example 1
![{\displaystyle f'(x)=x^{2}{\sqrt[{2}]{4-9x}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/39dc3fd3ace4dd663f4ce115bbbf198b994b2934)
example 2
simplify
Chain rule ![{\displaystyle [f(g(x))]'=f'(g(x))*g'(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c54bd493d6878d3b0c6779a32bb44dafdd87335e)
![{\displaystyle 2x{\sqrt[{2}]{4-9x}}+{-9 \over 2}{(4-9x)}^{-1 \over 2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/68423ce3b8c18c73b83e8976bc142b9669184ac1)
![{\displaystyle {x(8-{45x \over 2}){\sqrt[{2}]{4-9x}} \over {\sqrt[{2}]{4-9x}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cae0c8b41f737c4693f24f31ca69b2e92385ce7f)