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Popular >

derivative of arctan^2(x^3)

Solution

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

Solution

\frac{6 x ^{2} arctan ( x ^{3} )}{x ^{6} + 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (arctan (x^{3})) = \frac{3 x ^{2}}{x ^{6} + 1}

= 2 arctan (x^{3}) \frac{3 x ^{2}}{x ^{6} + 1}

Simplify

2 arctan (x^{3}) \frac{3 x ^{2}}{x ^{6} + 1} : \frac{6 x ^{2} arctan ( x ^{3} )}{x ^{6} + 1}

= \frac{6 x ^{2} arctan ( x ^{3} )}{x ^{6} + 1}

Popular Examples

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tangent of f(x)= 1/(2sqrt(x+!))tangent of

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area 4x^2,x^2+3 area

4 x^{2}, x^{2} + 3

y^'=(2x)/(y+x^2y)

y^{^{'}} = \frac{2 x}{y + x ^{2} y}

Frequently Asked Questions (FAQ)

What is the derivative of arctan^2(x^3) ?
The derivative of arctan^2(x^3) is (6x^2arctan(x^3))/(x^6+1)
What is the first derivative of arctan^2(x^3) ?
The first derivative of arctan^2(x^3) is (6x^2arctan(x^3))/(x^6+1)