Question

How do you get the derivative of y=3(x^2 + 2x)^2 using the chain rule. Please show step by step.

Answer 1

\(\large y=3(x^2 + 2x)^2 \)
You first take the derivative of the outer, then take the derivative of the inside.
Hint: The outer needs just the power rule and the inner needs the power rule as well. I will start by taking the derivative of the outer.
\(\large \frac{dy}{dx}=3*2((x^2 + 2x))^{2-1} *\frac{d}{dx}(x^2 + 2x)\)

Answer 2

Can you finish it from there?

Answer 3

Chain rule is done my taken the derivative of the outer and multiply the inner derivatives.

Answer 4

Yes, thank you!

Answer 5

\(\frac{dy}{dx}=\frac{d}{dx}3(x^2 + 2x)^{2}*\frac{d}{dx}(x^2 + 2x)\)

Answer 6

No problem!