What is the derivative of y=(arctan(2x))/x ?

The derivative of y=(arctan(2x))/x is (2x-arctan(2x)(4x^2+1))/(x^2(4x^2+1))

What is the first derivative of y=(arctan(2x))/x ?

The first derivative of y=(arctan(2x))/x is (2x-arctan(2x)(4x^2+1))/(x^2(4x^2+1))

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derivative of

y = \frac{arctan ( 2 x )}{x}

\frac{2 x - arctan ( 2 x ) ( 4 x ^{2} + 1 )}{x ^{2} ( 4 x ^{2} + 1 )}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( arctan ( 2 x ) ) x - \frac{d x}{d x} arctan ( 2 x )}{x ^{2}}

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

\frac{d x}{d x} = 1

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

Simplify

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

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

\frac{\partial}{\partial x} (\frac{x ^{2} + y ^{2}}{z ^{2}})

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

h \to 0 lim (- 2 x - h + 8)

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

n = 5 \sum \infty \frac{2}{( n ^{2} - 1 )}

What is the derivative of y=(arctan(2x))/x ?
The derivative of y=(arctan(2x))/x is (2x-arctan(2x)(4x^2+1))/(x^2(4x^2+1))
What is the first derivative of y=(arctan(2x))/x ?
The first derivative of y=(arctan(2x))/x is (2x-arctan(2x)(4x^2+1))/(x^2(4x^2+1))