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Popular >

derivative of e^{arcsin(x)}

Solution

derivative of

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

Solution

\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}}

Popular Examples

(dy)/(dx)=-1/(2y)

\frac{d y}{d x} = - \frac{1}{2 y}

integral from-1 to 1 of-2y^2+2

\int_{- 1}^{1} - 2 y^{2} + 2 d y

y^{''}+18y^'+80y=0

y^{^{''}} + 18 y^{^{'}} + 80 y = 0

integral from 0 to 1 of (25)/(x^5)

\int_{0}^{1} \frac{25}{x ^{5}} d x

integral from-3 to 0 of 9/(9x+4)

\int_{- 3}^{0} \frac{9}{9 x + 4} d x

Frequently Asked Questions (FAQ)

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))