Question

Derivada 3.(1-x/5)^3?

Answer 1

$f(x)=3\left[1-\dfrac{x}{5}\right]^{3}\\\\\\f(x)=3u^{3}$

Derivando como fiz anteriormente:

$f'(x)=\dfrac{d~3u^{3}}{dx}\cdot\dfrac{du}{dx}\\\\\\f'(x)=3\cdot3u^{3-1}\cdot\dfrac{du}{dx}\\\\\\f'(x)=9u^{2}\cdot \dfrac{du}{dx}\\\\\\f'(x)=9\left[1-\dfrac{x}{5}\right]^{2}\cdot\dfrac{d\left(1-\frac{x}{5}\right)}{dx}\\\\\\f'(x)=9\left[1-\dfrac{x}{5}\right]^{2}\cdot\left(-\dfrac{1}{5}\right)\\\\\\\boxed{\boxed{f'(x)=-\dfrac{9}{5}\left[1-\dfrac{x}{5}\right]^{2}}}$

Se preferir simplificar mais:

$f'(x)=-\dfrac{9}{5}\left[\dfrac{5-x}{5}\right]^{2}\\\\\\f'(x)=-\dfrac{9}{5}\cdot\dfrac{(5-x)^{2}}{5^{2}}\\\\\\f'(x)=-\dfrac{9}{5\cdot25}\cdot(5-x)^{2}\\\\\\\boxed{\boxed{f'(x)=-\dfrac{9}{125}(5-x)^{2}}}$