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Popular >

derivative of (arctan(5x))^2

Solution

derivative of

(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

derivative of sqrt(x-2)+sqrt(y-1)

\frac{d}{d x} (x - 2 + y - 1)

limit as x approaches 1+of (x+10)/(1-x)

x \to 1 + lim (\frac{x + 10}{1 - x})

tangent of x^2+xy+y^2=3,(1,1)tangent of

x^{2} + x y + y^{2} = 3, (1, 1)

limit as x approaches 7 of ((x^2-5x-14))/(x-7)

x \to 7 lim (\frac{( x ^{2} - 5 x - 14 )}{x - 7})

y^'+1/(200+t)y=0,y(0)=60

y^{^{'}} + \frac{1}{200 + t} y = 0, y (0) = 60

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)