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Popular >

derivative of y= x/(x-5)

Solution

derivative of

y = \frac{x}{x - 5}

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

Popular Examples

integral of 1/x*1/x

\int \frac{1}{x} \cdot \frac{1}{x} d x

integral from 0 to 7 of sqrt(x^2-49)

\int_{0}^{7} x^{2} - 49 d x

x(dy)/(dx)=y+2sqrt(xy)

x \frac{d y}{d x} = y + 2 x y

(d^2)/(dx^2)(sqrt(x^2+64))

\frac{d ^{2}}{d x ^{2}} (x^{2} + 64)

(dy)/(dx)+0.7x=18.2

\frac{d y}{d x} + 0.7 x = 18.2

Frequently Asked Questions (FAQ)

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