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

1. Zale101

$$\large y=3(x^2 + 2x)^2$$ 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. $$\large \frac{dy}{dx}=3*2((x^2 + 2x))^{2-1} *\frac{d}{dx}(x^2 + 2x)$$

2. Zale101

Can you finish it from there?

3. Zale101

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

4. anonymous

Yes, thank you!

5. Zale101

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

6. Zale101

No problem!