Difference between revisions of "Simplifying Derivatives"
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| Line 1: | Line 1: | ||
====example 1==== | ====example 1==== | ||
<math>f'(x)= x^2 \sqrt[2]{4-9x}</math> | |||
====example 2==== | |||
<math>f'(x)= x^2 \sqrt[2]{4-9x}</math> simplify | <math>f'(x)= x^2 \sqrt[2]{4-9x}</math> simplify | ||
| Line 6: | Line 9: | ||
<math>2x \sqrt[2]{4-9x} + {-9 \over 2} {(4-9x)}^{-1 \over 2} </math> | <math>2x \sqrt[2]{4-9x} + {-9 \over 2} {(4-9x)}^{-1 \over 2} </math> | ||
<math> { x (8 - { 45x \over 2} ) \sqrt[2]{4-9x} \over \sqrt[2]{4-9x} </math> | <math> { x (8 - { 45x \over 2} ) \sqrt[2]{4-9x} \over \sqrt[2]{4-9x} }</math> | ||
Revision as of 14:28, 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)