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Popular >

derivative of y=(arctan(5x))^2

Solution

derivative of

y = (arctan (5 x))^{2}

Solution

\frac{10 arctan ( 5 x )}{25 x ^{2} + 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (arctan (5 x)) = \frac{5}{25 x ^{2} + 1}

= 2 arctan (5 x) \frac{5}{25 x ^{2} + 1}

Simplify

2 arctan (5 x) \frac{5}{25 x ^{2} + 1} : \frac{10 arctan ( 5 x )}{25 x ^{2} + 1}

= \frac{10 arctan ( 5 x )}{25 x ^{2} + 1}

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Frequently Asked Questions (FAQ)

What is the derivative of y=(arctan(5x))^2 ?
The derivative of y=(arctan(5x))^2 is (10arctan(5x))/(25x^2+1)
What is the first derivative of y=(arctan(5x))^2 ?
The first derivative of y=(arctan(5x))^2 is (10arctan(5x))/(25x^2+1)