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

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Answer 1 · 2018-07-28T01:17:31

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

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}}#