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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

x \to \frac{x}{3} lim (sec (x))

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

\frac{d}{d x} (\frac{1}{3 x ^{2} + 5 x})

\int e^{- y^{2}} y d y

y^{^{'}} = 5 - y

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