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Popular Calculus >

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

Solution

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

Solution

- \frac{4 x}{( x - 2 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 x ( x - 2 ) ^{2} - 2 ( x - 2 ) x ^{2}}{( ( x - 2 ) ^{2} ) ^{2}} : - \frac{4 x}{( x - 2 ) ^{3}}

= - \frac{4 x}{( x - 2 ) ^{3}}

Graph

Popular Examples

y^{''}+3y^'+2y=sin(e^x)

y^{^{''}} + 3 y^{^{'}} + 2 y = sin (e^{x})

integral from 1 to 2 of 3/(sqrt(4x-x^2))

\int_{1}^{2} \frac{3}{4 x - x ^{2}} d x

tangent of f(x)=sqrt(x-4),\at x=13

t an g e n t f (x) = x - 4, at x = 13

y^{^{'}} = - \frac{2 x}{y}

(dy)/(dx)=(8x)/(5y)

\frac{d y}{d x} = \frac{8 x}{5 y}

Frequently Asked Questions (FAQ)

What is the ((x^2)/((x-2)^2))^' ?
The ((x^2)/((x-2)^2))^' is -(4x)/((x-2)^3)
What is the first ((x^2)/((x-2)^2))^' ?
The first ((x^2)/((x-2)^2))^' is -(4x)/((x-2)^3)