What is the derivative of this function 1/4arctan(x/4)?

1 Answer
mason m
Dec 6, 2016

1/(x^2+16)

Explanation:

It's helpful to know that d/dxarctan(x)=1/(x^2+1). Then, when there is a function within the arctangent function, we can apply the chain rule to see that d/dxarctan(f(x))=1/((f(x))^2+1)*f'(x).

Thus, d/dx1/4arctan(x/4)=1/4*1/((x/4)^2+1)*d/dx(x/4)

Continuing simplification, d/dx1/4arctan(x/4)=1/4*1/(x^2/16+1)*1/4

=1/16*1/((x^2+16)/16)

=1/16*16/(x^2+16)

=1/(x^2+16)

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