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Popular >

derivative of ((x+3/(x-1))^2)

Solution

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

Solution

- \frac{8 ( x + 3 )}{( x - 1 ) ^{3}}

Solution steps

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

Apply the chain rule:

2 \cdot \frac{x + 3}{x - 1} \frac{d}{d x} (\frac{x + 3}{x - 1})

= 2 \cdot \frac{x + 3}{x - 1} \frac{d}{d x} (\frac{x + 3}{x - 1})

\frac{d}{d x} (\frac{x + 3}{x - 1}) = - \frac{4}{( x - 1 ) ^{2}}

= 2 \cdot \frac{x + 3}{x - 1} (- \frac{4}{( x - 1 ) ^{2}})

Simplify

2 \cdot \frac{x + 3}{x - 1} (- \frac{4}{( x - 1 ) ^{2}}) : - \frac{8 ( x + 3 )}{( x - 1 ) ^{3}}

= - \frac{8 ( x + 3 )}{( x - 1 ) ^{3}}

Popular Examples

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

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

y^{''}-12y^'+61y=0

y^{^{''}} - 12 y^{^{'}} + 61 y = 0

(dy)/(dx)= y/x ln(y)

\frac{d y}{d x} = \frac{y}{x} ln (y)

integral from 0 to pi/2 of-6sin^2(3x)

\int_{0}^{\frac{π}{2}} - 6 sin^{2} (3 x) d x

(\partial)/(\partial x)(2xy(9-x-y))

\frac{\partial}{\partial x} (2 x y (9 - x - y))

Frequently Asked Questions (FAQ)

What is the derivative of ((x+3/(x-1))^2) ?
The derivative of ((x+3/(x-1))^2) is -(8(x+3))/((x-1)^3)
What is the first derivative of ((x+3/(x-1))^2) ?
The first derivative of ((x+3/(x-1))^2) is -(8(x+3))/((x-1)^3)