Question

find the derivative

y=(x^3 lnx)^4

Answer 1

First step is the easiest. Find the derivative of the outer shell. This will give us 4*(x^3*ln(x))^3. Next we are going to multiply that by the function inside the parentheses. Using the product rule, what is the derivative of the inside?

Answer 2

(3x^2 * 1/x)

Answer 3

im not sure if i did that right. nat logs throw me off.

Answer 4

whoops. one sec. forgot to do the product rule.

Answer 5

No worries! Another way that might help you thinking about this problem is to just instead distribute the exponent. That is probably easier than the method I showed you above. If you distribute the power you will get x^(12) * ln(x)^4 if that is any easier on you

Answer 6

so is the answer: \[4(x ^{3} lnx)^{3} (3x ^{2}lnx+x ^{2})\]

Answer 7

You got it :)

Answer 8

Awesome. Thanks man.