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Popular >

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

Solution

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

Solution

\frac{8 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}}

Expand

2 x (x^{2} + 1) - 2 x (x^{2} - 3) : 8 x

= \frac{8 x}{( x ^{2} + 1 ) ^{2}}

Popular Examples

integral from 1 to 5 of t^3ln(4t)

\int_{1}^{5} t^{3} ln (4 t) d t

integral of (x-1)/(x^2-2x+3)

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

derivative of 3x^{-1/2}derivative of

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

derivative of (7arcsin(4x)^x)

\frac{d}{d x} ((7 arcsin (4 x))^{x})

(\partial)/(\partial x)((zx-y)/(sqrt(x)))

\frac{\partial}{\partial x} (\frac{z x - y}{x})

Frequently Asked Questions (FAQ)

What is the derivative of (x^2-3/(x^2+1)) ?
The derivative of (x^2-3/(x^2+1)) is (8x)/((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 (8x)/((x^2+1)^2)