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)

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

\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}}

f (x) = e^{x}

y = 6 x^{2} + 3 x - 9

\int e^{- 2 u} d u

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

\int_{0}^{x^{2}} x sin (t^{2}) d t

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)