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Popular >

derivative of (sqrt(x)+1/(sqrt(x)-1))

Solution

\frac{d}{d x} (\frac{x + 1}{x - 1})

Solution

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

Solution steps

\frac{d}{d x} (\frac{x + 1}{x - 1})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial x)(tan(5+2x^2y^3z^2))

\frac{\partial}{\partial x} (tan (5 + 2 x^{2} y^{3} z^{2}))

derivative of (1+sin(x)*cos(2x))

\frac{d}{d x} ((1 + sin (x)) \cdot cos (2 x))

integral of (2x^2+3x+7)/(x^3+3x)

\int \frac{2 x ^{2} + 3 x + 7}{x ^{3} + 3 x} d x

(dy)/(dx)=(cos(x))e^{y+sin(x)},y(0)=0

\frac{d y}{d x} = (cos (x)) e^{y + s i n (x)}, y (0) = 0

y^{''}-3y^'+2y=0,y(0)=-1/5 ,y^'(0)=-8/5

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = - \frac{1}{5}, y^{^{'}} (0) = - \frac{8}{5}

Frequently Asked Questions (FAQ)

What is the derivative of (sqrt(x)+1/(sqrt(x)-1)) ?
The derivative of (sqrt(x)+1/(sqrt(x)-1)) is -1/(sqrt(x)(\sqrt{x)-1)^2}
What is the first derivative of (sqrt(x)+1/(sqrt(x)-1)) ?
The first derivative of (sqrt(x)+1/(sqrt(x)-1)) is -1/(sqrt(x)(\sqrt{x)-1)^2}