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Popular >

derivative of 4arctan(sqrt(x))

Solution

\frac{d}{d x} (4 arctan (x))

Solution

\frac{2}{x ( x + 1 )}

Solution steps

\frac{d}{d x} (4 arctan (x))

Take the constant out:

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

= 4 \frac{d}{d x} (arctan (x))

Apply the chain rule:

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

Simplify

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

= \frac{2}{x ( x + 1 )}

Popular Examples

(y-x)e^x+(1+e^x)y^'=0,y(1)=1

(y - x) e^{x} + (1 + e^{x}) y^{^{'}} = 0, y (1) = 1

implicit (dy)/(dx),50x^{1/3}y^{2/3}=600 implicit derivative

\frac{d y}{d x}, 50 x^{\frac{1}{3}} y^{\frac{2}{3}} = 600

f(x)=(4x)^{ln(4x)}

f (x) = (4 x)^{l n (4 x)}

integral from 1 to 2 of (13)/(x^3+3x)

\int_{1}^{2} \frac{13}{x ^{3} + 3 x} d x

limit as x approaches infinity of 2x^2-8

x \to \infty lim (2 x^{2} - 8)

Frequently Asked Questions (FAQ)

What is the derivative of 4arctan(sqrt(x)) ?
The derivative of 4arctan(sqrt(x)) is 2/(sqrt(x)(x+1))
What is the first derivative of 4arctan(sqrt(x)) ?
The first derivative of 4arctan(sqrt(x)) is 2/(sqrt(x)(x+1))