What is the derivative of In(x+1/(sqrt(x-1))) ?

The derivative of In(x+1/(sqrt(x-1))) is (nI(x-3))/(2(x-1)sqrt(x-1))

What is the first derivative of In(x+1/(sqrt(x-1))) ?

The first derivative of In(x+1/(sqrt(x-1))) is (nI(x-3))/(2(x-1)sqrt(x-1))

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

\frac{n I ( x - 3 )}{2 ( x - 1 ) x - 1}

Solution steps

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

Treat

n, I

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= I n \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}}

= I n \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) = 1

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

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

Simplify

I n \frac{1 \cdot x - 1 - \frac{1}{2 x - 1} ( x + 1 )}{( x - 1 ) ^{2}} : \frac{n I ( x - 3 )}{2 ( x - 1 ) x - 1}

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

\int x sin^{2} (2 x) d x

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

4 t^{3}

x \to \infty + lim (4 x)

[x + (x + sin^{2} (x))^{3}]^{6}

What is the derivative of In(x+1/(sqrt(x-1))) ?
The derivative of In(x+1/(sqrt(x-1))) is (nI(x-3))/(2(x-1)sqrt(x-1))
What is the first derivative of In(x+1/(sqrt(x-1))) ?
The first derivative of In(x+1/(sqrt(x-1))) is (nI(x-3))/(2(x-1)sqrt(x-1))