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Popular >

derivative of (arctan(x)^3)

Solution

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

Solution

\frac{3 arctan ^{2} ( x )}{x ^{2} + 1}

Solution steps

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

Apply the chain rule:

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

= 3 (arctan (x))^{2} \frac{d}{d x} (arctan (x))

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

= 3 (arctan (x))^{2} \frac{1}{x ^{2} + 1}

Simplify

3 arctan^{2} (x) \frac{1}{x ^{2} + 1} : \frac{3 arctan ^{2} ( x )}{x ^{2} + 1}

= \frac{3 arctan ^{2} ( x )}{x ^{2} + 1}

Popular Examples

(\partial)/(\partial x)(1/(f(x))-1/x)

\frac{\partial}{\partial x} (\frac{1}{f ( x )} - \frac{1}{x})

(\partial)/(\partial z)((x+y)/(z-2y))

\frac{\partial}{\partial z} (\frac{x + y}{z - 2 y})

derivative of sqrt(y^2+x^2)

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

integral of sin(1/7)x

\int sin (\frac{1}{7}) x d x

limit as h approaches 0 of (((h-5)^2-25))/((h))

h \to 0 lim \frac{( ( h - 5 ) ^{2} - 25 )}{( h )}

Frequently Asked Questions (FAQ)

What is the derivative of (arctan(x)^3) ?
The derivative of (arctan(x)^3) is (3arctan^2(x))/(x^2+1)
What is the first derivative of (arctan(x)^3) ?
The first derivative of (arctan(x)^3) is (3arctan^2(x))/(x^2+1)