How do you find the derivative of arcsin^3(5x)arcsin3(5x)?

1 Answer

f'(x)=\frac{15(\sin^{-1}(5x))^2}{\sqrt{1-(5x)^2}}

Explanation:

Given function:

f(x)=(\sin^{-1}(5x))^3

Differentiating above function w.r.t. x using chain rule as follows

d/dxf(x)=d/dx(\sin^{-1}(5x))^3

f'(x)=3(\sin^{-1}(5x))^2d/dx(sin^{-1}(5x))

=3(\sin^{-1}(5x))^2\frac{1}{\sqrt{1-(5x)^2}}d/dx(5x)

=3(\sin^{-1}(5x))^2\frac{1}{\sqrt{1-25x^2}}(5)

=\frac{15(\sin^{-1}(5x))^2}{\sqrt{1-(5x)^2}}