a ′ ( x ) = x 3 ( 2 x − 5 ) 4 {\displaystyle a'(x)=x^{3}{(2x-5)}^{4}}
Product Rule ( f ∗ g ) ′ = f ∗ g ′ + g ∗ f ′ {\displaystyle (f*g)'=f*g'+g*f'}
f = x 3 {\displaystyle f=x^{3}} f ′ = 3 x 2 {\displaystyle f'=3x^{2}} g = ( 2 x − 5 ) 4 {\displaystyle g={(2x-5)}^{4}} g ′ = 4 ( 2 x − 5 ) 3 ( 2 ) {\displaystyle g'=4{(2x-5)}^{3}(2)}
a ′ = ( x 3 ) ( 3 x 2 ) + ( ( 2 x − 5 ) 4 ) ( 4 ( 2 x − 5 ) 3 ( 2 ) ) {\displaystyle a'=(x^{3})(3x^{2})+({(2x-5)}^{4})(4{(2x-5)}^{3}(2))}
f ′ ( x ) = x 2 4 − 9 x 2 {\displaystyle f'(x)=x^{2}{\sqrt[{2}]{4-9x}}} simplify
Chain rule [ f ( g ( x ) ) ] ′ = f ′ ( g ( x ) ) ∗ g ′ ( x ) {\displaystyle [f(g(x))]'=f'(g(x))*g'(x)}
2 x 4 − 9 x 2 + − 9 2 ( 4 − 9 x ) − 1 2 {\displaystyle 2x{\sqrt[{2}]{4-9x}}+{-9 \over 2}{(4-9x)}^{-1 \over 2}}
x ( 8 − 45 x 2 ) 4 − 9 x 2 4 − 9 x 2 {\displaystyle {x(8-{45x \over 2}){\sqrt[{2}]{4-9x}} \over {\sqrt[{2}]{4-9x}}}}
![{\displaystyle f'(x)=x^{2}{\sqrt[{2}]{4-9x}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/39dc3fd3ace4dd663f4ce115bbbf198b994b2934)
simplify
![{\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)