Question

how can i take the derivative of this function ?
f(x) =1/2x ln(x4), NOTE: this is all one thing together the two are being multiplied which is the confusing part. i can easily take the derivative of 1/2x by itself but the combination is difficult. do i do u substitutioon?

Answer 1

oh and its ln(x^4)

Answer 2

is it like this?
\[\frac{1}{2}x\ln(x^4)\]

Answer 3

its a little hard to tell whats in the denominator and what isnt.

Answer 4

yes!

Answer 5

because i am supposed to take the derivative and then use that to find the equation of the tangent line.

Answer 6

so you are going to use a combination of the product rule and chain rule.

the 1/2 doesnt really matter, it will go to the front anyways. So let:
\[f(x) = x, g(x) = \ln(x^4)\] then using the product rule we get:
\[f'(x) = 1, g'(x) = \frac{1}{x^4}*4x^3 = \frac{4}{x}\]
\[(f(x)g(x))' = f'(x)g(x)+f(x)g'(x)\]\[(x\ln(x^4))'= \ln(x^4)+x*\frac{4}{x} = \ln(x^4) + 4\]

Answer 7

So putting that 1/2 back in front we get:
\[\frac{1}{2}(\ln(x^4)+4)\]

Answer 8

oki

Answer 9

n then what