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Popular >

derivative of e^xarcsin(x)

Solution

\frac{d}{d x} (e^{x} arcsin (x))

Solution

e^{x} arcsin (x) + \frac{e ^{x}}{1 - x ^{2}}

Solution steps

\frac{d}{d x} (e^{x} arcsin (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = arcsin (x)

= \frac{d}{d x} (e^{x}) arcsin (x) + \frac{d}{d x} (arcsin (x)) e^{x}

\frac{d}{d x} (e^{x}) = e^{x}

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

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

\frac{1}{1 - x ^{2}} e^{x} = \frac{e ^{x}}{1 - x ^{2}}

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

Popular Examples

integral from-2 to 3 of x

\int_{- 2}^{3} x d x

integral from 0 to 2 of (x^2-3x)

\int_{0}^{2} (x^{2} - 3 x) d x

derivative of (x^2-7x+10/(3x^2-15x))

\frac{d}{d x} (\frac{x ^{2} - 7 x + 10}{3 x ^{2} - 15 x})

tangent of f(x)=(2x+5)/(5x-1),\at x=-1 tangent of

f (x) = \frac{2 x + 5}{5 x - 1}, at x = - 1

integral of (x^2+6x)/(x^3-x^2+x-1)

\int \frac{x ^{2} + 6 x}{x ^{3} - x ^{2} + x - 1} d x

Frequently Asked Questions (FAQ)

What is the derivative of e^xarcsin(x) ?
The derivative of e^xarcsin(x) is e^xarcsin(x)+(e^x)/(sqrt(1-x^2))
What is the first derivative of e^xarcsin(x) ?
The first derivative of e^xarcsin(x) is e^xarcsin(x)+(e^x)/(sqrt(1-x^2))