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Popular >

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

Solution

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

Solution

- \frac{8 ( x + 2 )}{( x - 2 ) ^{3}}

Solution steps

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

Apply the chain rule:

2 \cdot \frac{x + 2}{x - 2} \frac{d}{d x} (\frac{x + 2}{x - 2})

= 2 \cdot \frac{x + 2}{x - 2} \frac{d}{d x} (\frac{x + 2}{x - 2})

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

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

Simplify

2 \cdot \frac{x + 2}{x - 2} (- \frac{4}{( x - 2 ) ^{2}}) : - \frac{8 ( x + 2 )}{( x - 2 ) ^{3}}

= - \frac{8 ( x + 2 )}{( x - 2 ) ^{3}}

Popular Examples

integral of (x-sqrt(x)+1)(sqrt(x)+1)

\int (x - x + 1) (x + 1) d x

12x^3-3y^2sqrt(x^4+1)(dy)/(dx)=0

12 x^{3} - 3 y^{2} x^{4} + 1 \frac{d y}{d x} = 0

(\partial)/(\partial x)(cos^5(x^3y^8))

\frac{\partial}{\partial x} (cos^{5} (x^{3} y^{8}))

(d^2y)/(dx^2)=-y

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

derivative of f(x)=x^2(3-x)^2 derivative of

f (x) = x^{2} (3 - x)^{2}

Frequently Asked Questions (FAQ)

What is the derivative of ((x+2/(x-2))^2) ?
The derivative of ((x+2/(x-2))^2) is -(8(x+2))/((x-2)^3)
What is the first derivative of ((x+2/(x-2))^2) ?
The first derivative of ((x+2/(x-2))^2) is -(8(x+2))/((x-2)^3)