What is the derivative of ln(x^3 • sin x ^2)?

1 Answer
Øko
Apr 10, 2018

#dy/dx=3/x+2xcos(x^2)1/(sin(x^2))#

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)#

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