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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

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

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

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

Expand

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

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

Popular Examples

sum from n=2 to infinity of 1/(n^2-1)

n = 2 \sum \infty \frac{1}{n ^{2} - 1}

(\partial)/(\partial z)(ln(x+2y+3z))

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

limit as x approaches 3 of (x^2+x)/(x-3)

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

integral from 0 to k of 1/2 (e^x-1)

\int_{0}^{k} \frac{1}{2} (e^{x} - 1) d x

integral of xcsc^2(3x)

\int x csc^{2} (3 x) d x

Frequently Asked Questions (FAQ)

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