What is the derivative of e^{arcsin(x}) ?

The derivative of e^{arcsin(x}) is (e^{arcsin(x)})/(sqrt(1-x^2))

What is the first derivative of e^{arcsin(x}) ?

The first derivative of e^{arcsin(x}) is (e^{arcsin(x)})/(sqrt(1-x^2))

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\frac{d}{d x} (e^{a r c s i n (x)})

\frac{e ^{a r c s i n (x)}}{1 - x ^{2}}

Solution steps

\frac{d}{d x} (e^{a r c s i n (x)})

Apply the chain rule:

e^{a r c s i n (x)} \frac{d}{d x} (arcsin (x))

= e^{a r c s i n (x)} \frac{d}{d x} (arcsin (x))

\frac{d}{d x} (arcsin (x)) = \frac{1}{1 - x ^{2}}

= e^{a r c s i n (x)} \frac{1}{1 - x ^{2}}

Simplify

e^{a r c s i n (x)} \frac{1}{1 - x ^{2}} : \frac{e ^{a r c s i n (x)}}{1 - x ^{2}}

= \frac{e ^{a r c s i n (x)}}{1 - x ^{2}}

What is the derivative of e^{arcsin(x}) ?
The derivative of e^{arcsin(x}) is (e^{arcsin(x)})/(sqrt(1-x^2))
What is the first derivative of e^{arcsin(x}) ?
The first derivative of e^{arcsin(x}) is (e^{arcsin(x)})/(sqrt(1-x^2))