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Popular >

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

Solution

derivative of

f (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

limit as x approaches-2 of x^2-4/(x+2)

x \to - 2 lim (x^{2} - \frac{4}{x + 2})

area y=cos(x),y=0.5,0<= x<= pi area

y = cos (x), y = 0.5, 0 \leq x \leq π

1296y^{''}+1368y^'+361y=0

1296 y^{^{''}} + 1368 y^{^{'}} + 361 y = 0

x(dy)/(dx)=y+(x^2-2)^2

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

integral of sin^2(pix)cos^5(pix)

\int sin^{2} (π x) cos^{5} (π x) d x

Frequently Asked Questions (FAQ)

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