Question

attempt 1: 10 attempts remaining. compute the derivative of the function $y = 0.4(2x^{2}+3x - 5)^{5}$ using the chain rule. $\frac{dy}{dx}=$

Explanation:

Step1: Let $u = 2x^{2}+3x - 5$.

$y = 0.4u^{5}$

Step2: Differentiate $y$ with respect to $u$.

$\frac{dy}{du}=0.4\times5u^{4}=2u^{4}$

Step3: Differentiate $u$ with respect to $x$.

$\frac{du}{dx}=(2x^{2}+3x - 5)'=4x + 3$

Step4: Apply the Chain - Rule $\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$.

$\frac{dy}{dx}=2u^{4}\cdot(4x + 3)$

Step5: Substitute $u = 2x^{2}+3x - 5$ back in.

$\frac{dy}{dx}=2(2x^{2}+3x - 5)^{4}\cdot(4x + 3)$

Answer:

$2(4x + 3)(2x^{2}+3x - 5)^{4}$