What is the derivative of (x^2+x/(x^2+4x)) ?

The derivative of (x^2+x/(x^2+4x)) is 3/((x+4)^2)

What is the first derivative of (x^2+x/(x^2+4x)) ?

The first derivative of (x^2+x/(x^2+4x)) is 3/((x+4)^2)

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

\frac{3}{( x + 4 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( 2 x + 1 ) ( x ^{2} + 4 x ) - ( 2 x + 4 ) ( x ^{2} + x )}{( x ^{2} + 4 x ) ^{2}} : \frac{3}{( x + 4 ) ^{2}}

= \frac{3}{( x + 4 ) ^{2}}

\frac{d}{d x} (a e^{x} cos (x) + b e^{x} sin (x))

\int \frac{14 x ^{2} + 9 x + 43}{( x + 2 ) ( x ^{2} + 5 )} d x

\int + sin^{2} (6 x) cos^{2} (6 x) d x

\int [\frac{1}{x ^{2}} + sec^{2} (π x)] d x

What is the derivative of (x^2+x/(x^2+4x)) ?
The derivative of (x^2+x/(x^2+4x)) is 3/((x+4)^2)
What is the first derivative of (x^2+x/(x^2+4x)) ?
The first derivative of (x^2+x/(x^2+4x)) is 3/((x+4)^2)