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

The derivative of (x+1)/x is -1/(x^2)

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

The first derivative of (x+1)/x is -1/(x^2)

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derivative of

\frac{x + 1}{x}

- \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}}

f a c t or 4 - t^{2}

x \to 2 - lim (3 x^{2} - 12)

\int \frac{1}{x ^{2} + c ^{2}} d x

x y^{^{'}} + y = - 6 x y^{2}, y (1) = 9

t an g e n t f (x) = \frac{1}{x}, at x = 4

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