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Popular >

derivative of (x+2/(x-4))

Solution

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

Solution

- \frac{6}{( x - 4 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x + 2) = 1

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

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

Simplify

\frac{1 \cdot ( x - 4 ) - 1 \cdot ( x + 2 )}{( x - 4 ) ^{2}} : - \frac{6}{( x - 4 ) ^{2}}

= - \frac{6}{( x - 4 ) ^{2}}

Popular Examples

derivative of-2ab^2e^{-b^2x^2}x derivative of

- 2 a b^{2} e^{- b^{2} x^{2}} x

derivative of (x^3e^{(3x)})

\frac{d}{d x} ((x)^{3} e^{(3 x)})

y^2x^3dy-(x^3+1)dx=0

y^{2} x^{3} d y - (x^{3} + 1) d x = 0

-2(dy)/(dx)+6x^2=0

- 2 \frac{d y}{d x} + 6 x^{2} = 0

(\partial)/(\partial x)(x^2y^4)

\frac{\partial}{\partial x} (x^{2} y^{4})

Frequently Asked Questions (FAQ)

What is the derivative of (x+2/(x-4)) ?
The derivative of (x+2/(x-4)) is -6/((x-4)^2)
What is the first derivative of (x+2/(x-4)) ?
The first derivative of (x+2/(x-4)) is -6/((x-4)^2)