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

1 Answer
Luke Phillips
Jul 19, 2017

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

Explanation:

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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