What is the derivative of ln(x^3 • sin x ^2)?
1 Answer
Apr 10, 2018
Explanation:
We want to find the derivative of
y=ln(x^3sin(x^2))
Using the properties of logarithms
y=ln(x^3)+ln(sin(x^2))
color(white)(y)=3ln(x)+ln(sin(x^2))
By the chain rule
dy/dx=3/x+(d/dx(sin(x^2)))1/(sin(x^2))
color(white)(dy/dx)=3/x+2xcos(x^2)1/(sin(x^2))
color(white)(dy/dx)=3/x+2xcot(x^2)