What is the derivative of (x^2/(2x^2+x+1)) ?

The derivative of (x^2/(2x^2+x+1)) is (x^2+2x)/((2x^2+x+1)^2)

What is the first derivative of (x^2/(2x^2+x+1)) ?

The first derivative of (x^2/(2x^2+x+1)) is (x^2+2x)/((2x^2+x+1)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

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

\frac{\partial}{\partial x} (4 y^{3} sin (2 x))

\int \frac{1}{( 3 x - 1 ) ^{3}} d x

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

\frac{d}{d x} ((a x^{2} + b x + c) e^{\frac{- x}{8}})

\int \frac{x ^{2} - 2 x + 3}{x ^{3} + 3 x} d x

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