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Popular >

derivative of arctan(sqrt(x^3))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of arcsin(5x^2)

\frac{d}{d x} (arcsin (5 x^{2}))

(\partial)/(\partial x)(x^2y-1)

\frac{\partial}{\partial x} (x^{2} y - 1)

y^'=(2y+1)cot(x)

y^{^{'}} = (2 y + 1) cot (x)

derivative of (3x^2/(x^2+1))

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

derivative of y=(sqrt(x)-2)/(sqrt(x)+2)derivative of

y = \frac{x - 2}{x + 2}

Frequently Asked Questions (FAQ)

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