# Thread: Logarithmic Differentiation

1. ## Logarithmic Differentiation

Use logarithmic differentiation to find the derivative of the function:
$\displaystyle y=3x^{cos(4x)}$

This is the steps I took:
$\displaystyle ln(y)=ln(3x^{cos(4x)})$
$\displaystyle ln(y)=ln(3)+cos(4x)ln(x)$
$\displaystyle \frac{y'}{y}=1/3+(-4sin(4x)ln(x)+cos(4x)\frac{1}{x})$
$\displaystyle y'=3x^{cos(4x)}(\frac{1}{3}-4sin(4x)ln(x)+cos(4x)\frac{1}{x})$
$\displaystyle y'=x^{cos(4x)}-\frac{4}{3}sin(4x)ln(x)x^{cos(4x)}+3cos4x^{cos(4x)-1)}$

What did I do wrong?

2. ln(3) is a number.
the derivative of a number is 0.