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Popular >

derivative of (x+4/(x-4))

Solution

\frac{d}{d x} (\frac{x + 4}{x - 4})

Solution

- \frac{8}{( x - 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x + 4}{x - 4})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x + 4) = 1

\frac{d}{d x} (x - 4) = 1

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

Simplify

\frac{1 \cdot ( x - 4 ) - 1 \cdot ( x + 4 )}{( x - 4 ) ^{2}} : - \frac{8}{( x - 4 ) ^{2}}

= - \frac{8}{( x - 4 ) ^{2}}

Popular Examples

integral of-cos^2(x)sin(x)

\int - cos^{2} (x) sin (x) d x

integral of (5cos(x)+4sin(x))

\int (5 cos (x) + 4 sin (x)) d x

derivative of x/(tan(3x-1))

\frac{d}{d x} (\frac{x}{tan ( 3 x - 1 )})

integral of (ln(y))/(xy)

\int \frac{ln ( y )}{x y} d y

sum from n=1 to infinity of 1/(2n^3)

n = 1 \sum \infty \frac{1}{2 n ^{3}}

Frequently Asked Questions (FAQ)

What is the derivative of (x+4/(x-4)) ?
The derivative of (x+4/(x-4)) is -8/((x-4)^2)
What is the first derivative of (x+4/(x-4)) ?
The first derivative of (x+4/(x-4)) is -8/((x-4)^2)