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Popular >

derivative of (x^2/((x-1)^2))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= - \frac{2 x}{( x - 1 ) ^{3}}

Popular Examples

derivative of 5sec(xtan(x))

\frac{d}{d x} (5 sec (x) tan (x))

limit as u approaches 8 of ((u^2-5u-24))/(u-8)

u \to 8 lim (\frac{( u ^{2} - 5 u - 24 )}{u - 8})

(\partial)/(\partial x)(3+200x^2+300y^2)

\frac{\partial}{\partial x} (3 + 200 x^{2} + 300 y^{2})

tangent of f(x)=((2x-1))/(x+3),\at x=2 tangent of

f (x) = \frac{( 2 x - 1 )}{x + 3}, at x = 2

derivative of f(x)=(2x-4)^4(x^2+x+1)^5 derivative of

f (x) = (2 x - 4)^{4} (x^{2} + x + 1)^{5}

Frequently Asked Questions (FAQ)

What is the derivative of (x^2/((x-1)^2)) ?
The derivative of (x^2/((x-1)^2)) is -(2x)/((x-1)^3)
What is the first derivative of (x^2/((x-1)^2)) ?
The first derivative of (x^2/((x-1)^2)) is -(2x)/((x-1)^3)