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Popular >

derivative of (arctan(5x)^2)

Solution

\frac{d}{d x} ((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}

Popular Examples

integral of (x^4+8x^2+8)/(x^3-4x)

\int \frac{x ^{4} + 8 x ^{2} + 8}{x ^{3} - 4 x} d x

taylor x^3-3x^2+5x-7,0 taylor

x^{3} - 3 x^{2} + 5 x - 7, 0

slope of (1.7)(3.3)slope

(1.7) (3.3)

integral from 0 to 2 of ()/(sqrt(4+t^2))

\int_{0}^{2} \frac{d t}{4 + t ^{2}} d x

y^{''}+49y=0,y(0)=4,y^'(0)=-6

y^{^{''}} + 49 y = 0, y (0) = 4, y^{^{'}} (0) = - 6

Frequently Asked Questions (FAQ)

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