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Popular >

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

Solution

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

Solution

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

Solution steps

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

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

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

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

Simplify

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

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

Popular Examples

derivative of (x/(y^2)-(y/(x^2)))

\frac{d}{d x} ((\frac{x}{y ^{2}}) - (\frac{y}{x ^{2}}))

y^'+5y=4,y(0)=0

y^{^{'}} + 5 y = 4, y (0) = 0

derivative of (8x^2+302x/(x-10))

\frac{d}{d x} (\frac{8 x ^{2} + 302 x}{x - 10})

inverse oflaplace 1/(s+1)*1/s inverse laplace

\frac{1}{s + 1} \cdot \frac{1}{s}

(\partial)/(\partial y)(y+e^x)

\frac{\partial}{\partial y} (y + e^{x})

Frequently Asked Questions (FAQ)

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