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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

derivative of f(x)=(e^x-e^x)/(e^x+e^x)derivative of

f (x) = \frac{e ^{x} - e ^{x}}{e ^{x} + e ^{x}}

limit as x approaches-2 of x^2-3x+4

x \to - 2 lim (x^{2} - 3 x + 4)

integral from-infinity to 0 of z/(z^4+4)

\int_{- \infty}^{0} \frac{z}{z ^{4} + 4} d z

sum from n=0 to infinity of (-4/7)^n

n = 0 \sum \infty (- \frac{4}{7})^{n}

5 y^{^{''}} + 4 y^{^{'}} = 0

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)