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Popular >

derivative of (arctan(6x))^2

Solution

derivative of

(arctan (6 x))^{2}

Solution

\frac{12 arctan ( 6 x )}{36 x ^{2} + 1}

Solution steps

\frac{d}{d x} ((arctan (6 x))^{2})

Apply the chain rule:

2 arctan (6 x) \frac{d}{d x} (arctan (6 x))

= 2 arctan (6 x) \frac{d}{d x} (arctan (6 x))

\frac{d}{d x} (arctan (6 x)) = \frac{6}{36 x ^{2} + 1}

= 2 arctan (6 x) \frac{6}{36 x ^{2} + 1}

Simplify

2 arctan (6 x) \frac{6}{36 x ^{2} + 1} : \frac{12 arctan ( 6 x )}{36 x ^{2} + 1}

= \frac{12 arctan ( 6 x )}{36 x ^{2} + 1}

Popular Examples

(dy)/(dx)=-x/y ,y(4)=3

\frac{d y}{d x} = - \frac{x}{y}, y (4) = 3

(dy)/(dx)=e^{8x}+13y

\frac{d y}{d x} = e^{8 x} + 13 y

limit as x approaches pi/3 of (2cos^2(x)+3cos(x)-2)/(2cos(x)-1)

x \to \frac{π}{3} lim (\frac{2 cos ^{2} ( x ) + 3 cos ( x ) - 2}{2 cos ( x ) - 1})

derivative of f(x)=x^{-1/3}derivative of

f (x) = x^{- \frac{1}{3}}

integral of e^{5x+4}

\int e^{5 x + 4} d x

Frequently Asked Questions (FAQ)

What is the derivative of (arctan(6x))^2 ?
The derivative of (arctan(6x))^2 is (12arctan(6x))/(36x^2+1)
What is the first derivative of (arctan(6x))^2 ?
The first derivative of (arctan(6x))^2 is (12arctan(6x))/(36x^2+1)