I need to differentiate ln(x^4 sin(x^2) ). Help

[rcmango]

Homework Statement

need to differentiate:

f(x) = ln(x^4sinx^2)

Homework Equations

The Attempt at a Solution

just use ln 1/x and differentiate the sins and exponents to get what's below.

would this be the final form?
f'(x) = 4*(1/x) + 2*(cosx/(sinx)

 

[Shooting Star]

Correct.

(Yes, I think he meant sin^2 x, i.e. (sin x)^2.)

 

[HallsofIvy]

Homework Statement

need to differentiate:

f(x) = ln(x^4sinx^2)

Homework Equations

The Attempt at a Solution

just use ln 1/x and differentiate the sins and exponents to get what's below.

would this be the final form?

f'(x) = 4*(1/x) + 2*(cosx/(sinx)

I presume that the first thing you did was use the laws of logarithms to simplify
$f(x) = ln(x^4sin^2x)$ to $f(x)= 4 ln(x)+ 2 ln(sin(x)). Yes, the derivative is exactly what you say.$