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

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

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

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

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derivative of

\frac{2 x ^{2} - 1}{x + 1}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

t^{3}

f (x) = 20 x + \frac{420}{x}

f (x) = 2 x^{2} + 1

\int \frac{1}{( x - 3 ) x ^{2} - 6 x} d x

\int x^{7} ln (5 x) d x

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