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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

d er i v a t i v e b (1 - sin (x))

d er i v a t i v e \frac{4 cos ^{2} ( x )}{sin ^{2} ( x )}

d er i v a t i v e \frac{1}{r ^{3}}

d er i v a t i v e y = cos (5 x + 4)

d er i v a t i v e t^{0}

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