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Popular >

derivative of (x-5)/(x-2)

Solution

derivative of

\frac{x - 5}{x - 2}

Solution

\frac{3}{( x - 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 5}{x - 2})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot ( x - 2 ) - 1 \cdot ( x - 5 )}{( x - 2 ) ^{2}} : \frac{3}{( x - 2 ) ^{2}}

= \frac{3}{( x - 2 ) ^{2}}

Graph

Popular Examples

integral from 1 to infinity of x^{-5/2}

\int_{1}^{\infty} x^{- \frac{5}{2}} d x

(\partial)/(\partial x)((2x-2)^4(x^2+x+1)^5)

\frac{\partial}{\partial x} ((2 x - 2)^{4} (x^{2} + x + 1)^{5})

integral of x/(sqrt(9-x^2))

\int \frac{x}{9 - x ^{2}} d x

laplacetransform 4e^{-7t}*cos(9t)laplace transform

4 e^{- 7 t} \cdot cos (9 t)

derivative of f(x)=sin(x)-1/3 sin(3x)+1/5 sin(5x)derivative of

f (x) = sin (x) - \frac{1}{3} sin (3 x) + \frac{1}{5} sin (5 x)

Frequently Asked Questions (FAQ)

What is the derivative of (x-5)/(x-2) ?
The derivative of (x-5)/(x-2) is 3/((x-2)^2)
What is the first derivative of (x-5)/(x-2) ?
The first derivative of (x-5)/(x-2) is 3/((x-2)^2)