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

Answer 1

Charles Anctil

#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}}#

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Answer 2

Paisley Johnson

To find the derivative of arcsin^3(5x), you can use the chain rule. The derivative is 15 * (arcsin(5x))^2 * (1 / sqrt(1 - (5x)^2)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.