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How do you find the derivative of #2^arcsin(x)#?

Answer 1

Christopher Agresta

#"d"/("d"x) 2^{arcsin(x)} = (ln(2)2^{arcsin(x)})/(sqrt(1-x^2))#.

Rewrite #2^arcsin(x)=e^{ln(2)arcsin(x)}#.

Then, by the chain rule,

#"d"/("d"x) 2^{arcsin(x)} = ln(2) "d"/("d"x) (arcsin(x)) e^{ln(2)arcsin(x)}#.

The standard result for the derivative of #arcsin(x)# is #"d"/("d"x) (arcsin(x)) = 1/sqrt(1-x^2)#.

Then we see that,

#"d"/("d"x) 2^{arcsin(x)} = (ln(2)2^{arcsin(x)})/(sqrt(1-x^2))#.

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Answer 2

Elijah Abram

To find the derivative of ( 2^{\arcsin(x)} ), you can use the chain rule. The derivative is:

[ \frac{d}{dx} \left( 2^{\arcsin(x)} \right) = 2^{\arcsin(x)} \cdot \frac{d}{dx} (\arcsin(x)) \cdot \frac{1}{\sqrt{1 - x^2}} ]

So, the derivative is ( \frac{2^{\arcsin(x)}}{\sqrt{1 - x^2}} ).

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Answer from HIX Tutor

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