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Whats the derivative of #sin^-1 * (5x)#?

Answer 1

Charles Arocha

See explanation

Set #arcsinx=cos^(-1)x# hence we know that

#d((arcsinx))/dx=1/(sqrt(1-x^2)#

hence for a function #u(x)#

#d(arcsinu(x))/dx=1/sqrt(1-u^2(x))*du/dx#

hence for #u=5x# we get

#d(arcsin5x)/dx=5/(sqrt(1-25x^2))#

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Answer 2

Evelyn Agard

The derivative of ( \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.

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