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Popular >

derivative of (x+5/(x-5))

Solution

\frac{d}{d x} (\frac{x + 5}{x - 5})

Solution

- \frac{10}{( x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x + 5}{x - 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 5 ) ( x - 5 ) - \frac{d}{d x} ( x - 5 ) ( x + 5 )}{( x - 5 ) ^{2}}

\frac{d}{d x} (x + 5) = 1

\frac{d}{d x} (x - 5) = 1

= \frac{1 \cdot ( x - 5 ) - 1 \cdot ( x + 5 )}{( x - 5 ) ^{2}}

Simplify

\frac{1 \cdot ( x - 5 ) - 1 \cdot ( x + 5 )}{( x - 5 ) ^{2}} : - \frac{10}{( x - 5 ) ^{2}}

= - \frac{10}{( x - 5 ) ^{2}}

Popular Examples

y^'(x^2+1)+5x(y-1)=0,y(0)=7

y^{^{'}} (x^{2} + 1) + 5 x (y - 1) = 0, y (0) = 7

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x \to 0 lim (\frac{sin ( x )}{2})

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\int x^{4} \cdot e^{x^{5} + 2} d x

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5^{s i n (2 x)}

(dy)/(dx)=((x+xy))/((y+xy))

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Frequently Asked Questions (FAQ)

What is the derivative of (x+5/(x-5)) ?
The derivative of (x+5/(x-5)) is -(10)/((x-5)^2)
What is the first derivative of (x+5/(x-5)) ?
The first derivative of (x+5/(x-5)) is -(10)/((x-5)^2)