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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

integral of (1-tan(x))/(1+tan(x))

\int \frac{1 - tan ( x )}{1 + tan ( x )} d x

limit as x approaches 0 of ((x^3))/(x^3)

x \to 0 lim (\frac{( x ^{3} )}{x ^{3}})

derivative of (f(x))/(x^6)derivative of

\frac{f ( x )}{x ^{6}}

derivative of f(x)= t/(1+t)derivative of

f (x) = \frac{t}{1 + t}

limit as x approaches 0+of 3x

x \to 0 + lim (3 x)

Frequently Asked Questions (FAQ)

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