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Popular >

((x^2)/(x-5))^'

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

(x^{2})^{'} = 2 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}}

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Frequently Asked Questions (FAQ)

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