What is the derivative of (x^2+3/(sqrt(x^2+1))) ?

The derivative of (x^2+3/(sqrt(x^2+1))) is (x^3-x)/((x^2+1)sqrt(x^2+1))

What is the first derivative of (x^2+3/(sqrt(x^2+1))) ?

The first derivative of (x^2+3/(sqrt(x^2+1))) is (x^3-x)/((x^2+1)sqrt(x^2+1))

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

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

Solution steps

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

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

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

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

Simplify

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

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

What is the derivative of (x^2+3/(sqrt(x^2+1))) ?
The derivative of (x^2+3/(sqrt(x^2+1))) is (x^3-x)/((x^2+1)sqrt(x^2+1))
What is the first derivative of (x^2+3/(sqrt(x^2+1))) ?
The first derivative of (x^2+3/(sqrt(x^2+1))) is (x^3-x)/((x^2+1)sqrt(x^2+1))