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What is the derivative of this function #sin^-1 (5x)#?

Answer 1

Christopher Allers

#5/(sqrt(1-25x^2))#

#color(orange)"Reminder " d/dx(sin^-1x)=1/(sqrt(1-x^2))#

#"and " d/dx(sin^-1(f(x)))=(f'(x))/(sqrt(1-f(x)^2)#

#rArrd/dx(sin^-1(5x))#

#=5/(sqrt(1-(5x)^2))#

#=5/(sqrt(1-25x^2))#

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Answer 2

Ezra Adams

#(sin^(-1)(5x))'=5/sqrt(1-25x^2)#

Recall:

#(sin^(-1)u)'=1/sqrt(1-u^2)#

By the above rule (#u=5x#) along with Chain Rule,

#(sin^(-1)(5x))'=1/sqrt(1-(5x)^2)cdot(5x)' =5/sqrt(1-25x^2)#

I hope that this was clear.

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Answer 3

Elijah Abram

The derivative of the function ( \sin^{-1}(5x) ) is ( \frac{5}{\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.