What is the derivative of (x^n-1/(x-1)) ?

The derivative of (x^n-1/(x-1)) is (nx^n-nx^{n-1}-x^n+1)/((x-1)^2)

What is the first derivative of (x^n-1/(x-1)) ?

The first derivative of (x^n-1/(x-1)) is (nx^n-nx^{n-1}-x^n+1)/((x-1)^2)

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

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

Solution steps

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

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

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

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

Simplify

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

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

y = x 3600 - x^{2}

2 t^{3} cos (t)

\frac{\partial}{\partial z} (e^{x y z^{2} + z})

\int_{0}^{\frac{π}{4}} sin^{5} (2 x) d x

\frac{\partial}{\partial x} (4 x^{2} + 4 y^{3})

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