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Popular >

derivative of y=(x+1)/x

Solution

derivative of

y = \frac{x + 1}{x}

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d x}{d x} = 1

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

Simplify

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

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

Popular Examples

limit as x approaches-87 of F(x)

x \to - 87 lim (F (x))

integral from 0 to 1 of x^4e^{-x}

\int_{0}^{1} x^{4} e^{- x} d x

sum from n=0 to infinity of 5*3^n

n = 0 \sum \infty 5 \cdot 3^{n}

derivative of f(x)=(x^2-1)(x^2+1)derivative of

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n = 1 \sum \infty \frac{x ^{n}}{1 1 ^{n}}

Frequently Asked Questions (FAQ)

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