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Popular >

derivative of xarcsin(x)

Solution

\frac{d}{d 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}}

Graph

Popular Examples

derivative of tan(1+e^{2t})derivative of

tan (1 + e^{2 t})

(\partial)/(\partial x)(ln(5x^2+4y^2+9))

\frac{\partial}{\partial x} (ln (5 x^{2} + 4 y^{2} + 9))

integral of (12x^3)/(sqrt(2-x^4))

\int \frac{12 x ^{3}}{2 - x ^{4}} d x

derivative of f(x)=5x^4+1/((2x^2))derivative of

f (x) = 5 x^{4} + \frac{1}{( 2 x ^{2} )}

integral from-3 to 3 of sqrt(x^2+y^2)

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

Frequently Asked Questions (FAQ)

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