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Popular >

derivative of x/(x^2-15)

Solution

\frac{d}{d x} (\frac{x}{x ^{2} - 15})

Solution

\frac{- x ^{2} - 15}{( x ^{2} - 15 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} - 15})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d x}{d x} ( x ^{2} - 15 ) - \frac{d}{d x} ( x ^{2} - 15 ) x}{( x ^{2} - 15 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{2} - 15) = 2 x

= \frac{1 \cdot ( x ^{2} - 15 ) - 2 xx}{( x ^{2} - 15 ) ^{2}}

1 \cdot (x^{2} - 15) - 2 xx = - x^{2} - 15

= \frac{- x ^{2} - 15}{( x ^{2} - 15 ) ^{2}}

Popular Examples

integral of 9/((x-2)(x^2+4))

\int \frac{9}{( x - 2 ) ( x ^{2} + 4 )} d x

slope of (4.4)(5.9)slope

(4.4) (5.9)

y^{''}-y^'+16y=4sin(4t)

y^{^{''}} - y^{^{'}} + 16 y = 4 sin (4 t)

(\partial)/(\partial x)(9xsin(y-z))

\frac{\partial}{\partial x} (9 x sin (y - z))

derivative of 1/3 x^3+1/2 x^2+2

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

Frequently Asked Questions (FAQ)

What is the derivative of x/(x^2-15) ?
The derivative of x/(x^2-15) is (-x^2-15)/((x^2-15)^2)
What is the first derivative of x/(x^2-15) ?
The first derivative of x/(x^2-15) is (-x^2-15)/((x^2-15)^2)