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

The derivative of (x^2+3/(x^2+1)) is -(4x)/((x^2+1)^2)

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

The first derivative of (x^2+3/(x^2+1)) is -(4x)/((x^2+1)^2)

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

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

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) = 2 x

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

Simplify

\frac{2 x ( x ^{2} + 1 ) - 2 x ( x ^{2} + 3 )}{( x ^{2} + 1 ) ^{2}} : - \frac{4 x}{( x ^{2} + 1 ) ^{2}}

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

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

\frac{d}{d x} (\frac{2 x + 3}{x + 4})

x \to 4 lim (\frac{x - 4}{x - 4})

y = 5 x + 6

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

What is the derivative of (x^2+3/(x^2+1)) ?
The derivative of (x^2+3/(x^2+1)) is -(4x)/((x^2+1)^2)
What is the first derivative of (x^2+3/(x^2+1)) ?
The first derivative of (x^2+3/(x^2+1)) is -(4x)/((x^2+1)^2)