1. ## Derivatives

If I have f(x)=(x^4)ln(x^2+2), how do I find the derivative?

My thought:

Take the 1st x der. of 2nd + 2nd x der. of 1st?

(x^4) x (1/x^2+2) + ln(x^2+2) x (4x^3)

Which would then equal ????

If I have f(x)=(x^4)ln(x^2+2), how do I find the derivative?

My thought:

Take the 1st x der. of 2nd + 2nd x der. of 1st?

(x^4) x (1/x^2+2) + ln(x^2+2) x (4x^3)

Which would then equal ????
You are close. You just forgot to use the chain rule.

$\frac{d}{dx} \ln(x^2+2)=\frac{2x}{x^2+2}$

Besides that you are good. What do you mean "which would equal"?

$x^4 \cdot \frac{2x}{x^2+2} + 4x^3 \cdot \ln(x^2+2)$