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Popular >

derivative of arctan(ax^2)

Solution

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

Solution

\frac{2 a x}{a ^{2} x ^{4} + 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2 a x}{a ^{2} x ^{4} + 1}

Popular Examples

integral from 0 to 2 of (x+1)^2

\int_{0}^{2} (x + 1)^{2} d x

implicit (dy)/(dx),y^2=x^3 implicit derivative

\frac{d y}{d x}, y^{2} = x^{3}

limit as x approaches 0 of xln|x|

x \to 0 lim (x ln ∣ x ∣)

(\partial)/(\partial x)(e^{-4x^2})

\frac{\partial}{\partial x} (e^{- 4 x^{2}})

derivative of 6ln(x)

\frac{d}{d x} (6 ln (x))

Frequently Asked Questions (FAQ)

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