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Popular >

derivative of arctan(2x^2)

Solution

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

Solution

\frac{4 x}{4 x ^{4} + 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{4 x}{4 x ^{4} + 1}

Graph

Popular Examples

(\partial)/(\partial y)(y/(2x^2+y^2))

\frac{\partial}{\partial y} (\frac{y}{2 x ^{2} + y ^{2}})

integral of (4x^3-3x+5)

\int (4 x^{3} - 3 x + 5) d x

integral of x(1+x^2)^{-1/2}

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

limit as x approaches 1 of (x+2)/(x-1)

x \to 1 lim (\frac{x + 2}{x - 1})

derivative of e^{t/3}derivative of

e^{\frac{t}{3}}

Frequently Asked Questions (FAQ)

What is the derivative of arctan(2x^2) ?
The derivative of arctan(2x^2) is (4x)/(4x^4+1)
What is the first derivative of arctan(2x^2) ?
The first derivative of arctan(2x^2) is (4x)/(4x^4+1)