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

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Answer 1 · 2017-07-19T18:00:17

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

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,

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

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