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Popular >

derivative of 4arcsin(x^2)

Solution

derivative of

4 arcsin (x^{2})

Solution

\frac{8 x}{1 - x ^{4}}

Solution steps

\frac{d}{d x} (4 arcsin (x^{2}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (arcsin (x^{2}))

Apply the chain rule:

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

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

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

= 4 \cdot \frac{1}{1 - ( x ^{2} ) ^{2}} \cdot 2 x

Simplify

4 \cdot \frac{1}{1 - ( x ^{2} ) ^{2}} \cdot 2 x : \frac{8 x}{1 - x ^{4}}

= \frac{8 x}{1 - x ^{4}}

Popular Examples

integral from 0 to 6 of 1/(x^2-6x+5)

\int_{0}^{6} \frac{1}{x ^{2} - 6 x + 5} d x

derivative of Ate^{-t}

\frac{d}{d x} (A t e^{- t})

f (x) = e^{x^{6}}

(\partial)/(\partial y)(3y^2)

\frac{\partial}{\partial y} (3 y^{2})

derivative of (3/x ^{14})

\frac{d}{d x} ((\frac{3}{x})^{14})

Frequently Asked Questions (FAQ)

What is the derivative of 4arcsin(x^2) ?
The derivative of 4arcsin(x^2) is (8x)/(sqrt(1-x^4))
What is the first derivative of 4arcsin(x^2) ?
The first derivative of 4arcsin(x^2) is (8x)/(sqrt(1-x^4))