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Popular >

derivative of x^2arcsin(x)

Solution

\frac{d}{d x} (x^{2} arcsin (x))

Solution

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

Solution steps

\frac{d}{d x} (x^{2} arcsin (x))

Apply the Product Rule:

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

f = x^{2}, g = arcsin (x)

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

\frac{d}{d x} (x^{2}) = 2 x

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

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

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

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

Popular Examples

limit as x approaches 0 of y/x

x \to 0 lim (\frac{y}{x})

implicit (dy)/(dx),e^{x/y}=7x-y implicit derivative

\frac{d y}{d x}, e^{\frac{x}{y}} = 7 x - y

x y^{^{'}} - 2 y = x

sum from n=0 to infinity of (n2^n)/(3^n)

n = 0 \sum \infty \frac{n 2 ^{n}}{3 ^{n}}

derivative of y=x^3(2x-1)^5 derivative of

y = x^{3} (2 x - 1)^{5}

Frequently Asked Questions (FAQ)

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