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Popular >

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

Solution

derivative of

y = \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 h(t)=65-55cos((pit)/(15))derivative of

h (t) = 65 - 55 cos (\frac{π t}{15})

integral from-1 to 2 of (3x+1)

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

integral of 1/(x^3sqrt(x^2-49))

\int \frac{1}{x ^{3} x ^{2} - 49} d x

inverse oflaplace (x^2+1)/(x^2-x-6)inverse laplace

\frac{x ^{2} + 1}{x ^{2} - x - 6}

integral of ln(1+sqrt(x))

\int ln (1 + x) d x

Frequently Asked Questions (FAQ)

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