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Popular >

derivative of 2arctan(x^5)

Solution

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

Solution

\frac{10 x ^{4}}{x ^{10} + 1}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (arctan (x^{5}))

Apply the chain rule:

\frac{1}{( x ^{5} ) ^{2} + 1} \frac{d}{d x} (x^{5})

= \frac{1}{( x ^{5} ) ^{2} + 1} \frac{d}{d x} (x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

= 2 \cdot \frac{1}{( x ^{5} ) ^{2} + 1} \cdot 5 x^{4}

Simplify

2 \cdot \frac{1}{( x ^{5} ) ^{2} + 1} \cdot 5 x^{4} : \frac{10 x ^{4}}{x ^{10} + 1}

= \frac{10 x ^{4}}{x ^{10} + 1}

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Frequently Asked Questions (FAQ)

What is the derivative of 2arctan(x^5) ?
The derivative of 2arctan(x^5) is (10x^4)/(x^{10)+1}
What is the first derivative of 2arctan(x^5) ?
The first derivative of 2arctan(x^5) is (10x^4)/(x^{10)+1}