What's the derivative of f(x) = (1/3) (arctan(3x))^2?

1 Answer
mason m
Jan 31, 2016

f'(x)=(2arctan(3x))/(1+9x^2)

Explanation:

The first issue is the squared function. Use the chain rule:

f'(x)=2/3(arctan(3x))^1d/dx(arctan(3x))

To differentiate the arctan function, use the chain rule again. The general rule for arctan functions is d/dx(arctan(u))=(u')/(1+u^2). Here, u=3x, so

f'(x)=2/3arctan(3x)*3/(1+9x^2)

This simplifies to be

f'(x)=(2arctan(3x))/(1+9x^2)

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