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Popular >

derivative of f(x)=xarcsin(x)

Solution

derivative of

f (x) = x arcsin (x)

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = arcsin (x)

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

Popular Examples

limit as x approaches 0 of (x^2+2)/(x^2)

x \to 0 lim (\frac{x ^{2} + 2}{x ^{2}})

integral of (x-1)/(sqrt(x)+1)

\int \frac{x - 1}{x + 1} d x

(-(2x)/((x^2+1)^2))^'

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

tangent of f(x)=(64x)/(x^2+64),\at x=-4 tangent of

f (x) = \frac{64 x}{x ^{2} + 64}, at x = - 4

limit as x approaches 0+of sin(x)nx

x \to 0 + lim (sin (x) n x)

Frequently Asked Questions (FAQ)

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