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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{1}{4} x^{4} d x

\frac{d}{d x} (e^{- 2 x} - 2 e^{- 2 x} x)

\frac{d}{d t} (- 1 cos (t) + 8 sin (t))

\int_{0}^{1} 4 x - 4 x d x

\int \frac{x ^{5}}{( 3 - x ^{6} ) ^{4}} d x

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