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Popular Calculus >

derivative of ({r}(x)/x)

Solution

\frac{d}{d x} (\frac{r ( x )}{x})

Solution

\frac{x \frac{d}{d x} ( r ( x ) ) - r ( x )}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{r ( x )}{x})

Apply the Quotient Rule:

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

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

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

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

Simplify

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

Popular Examples

integral from 1 to 3 of (3x+2)^2

\int_{1}^{3} (3 x + 2)^{2} d x

(\partial)/(\partial x)(x/(3+6x^2+7y^2))

\frac{\partial}{\partial x} (\frac{x}{3 + 6 x ^{2} + 7 y ^{2}})

derivative of arcsin(xy)

\frac{d}{d x} (arcsin (x y))

f(x)=(xe^x)/(x+e^x)

f (x) = \frac{x e ^{x}}{x + e ^{x}}

integral of 4/((x+2)(x-2))

\int \frac{4}{( x + 2 ) ( x - 2 )} d x

Frequently Asked Questions (FAQ)

What is the derivative of ({r}(x)/x) ?
The derivative of ({r}(x)/x) is (x derivative of {r}(x)-{r}(x))/(x^2)
What is the first derivative of ({r}(x)/x) ?
The first derivative of ({r}(x)/x) is (x derivative of {r}(x)-{r}(x))/(x^2)