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Popular >

derivative of arctan(x^4)

Solution

\frac{d}{d x} (arctan (x^{4}))

Solution

\frac{4 x ^{3}}{x ^{8} + 1}

Solution steps

\frac{d}{d x} (arctan (x^{4}))

Apply the chain rule:

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

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

= \frac{1}{( x ^{4} ) ^{2} + 1} \cdot 4 x^{3}

Simplify

\frac{1}{( x ^{4} ) ^{2} + 1} \cdot 4 x^{3} : \frac{4 x ^{3}}{x ^{8} + 1}

= \frac{4 x ^{3}}{x ^{8} + 1}

Popular Examples

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f (t) = \frac{t ^{2} + 1}{t ^{2} - 1}

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\int_{1}^{\infty} \frac{1}{5 x + 2} d x

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\frac{d}{d x} (lo g_{7} (x^{2}))

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\frac{d}{d x} (6 (2 x - 9)^{5})

Frequently Asked Questions (FAQ)

What is the derivative of arctan(x^4) ?
The derivative of arctan(x^4) is (4x^3)/(x^8+1)
What is the first derivative of arctan(x^4) ?
The first derivative of arctan(x^4) is (4x^3)/(x^8+1)