What is the derivative of a{r}(xc,x) ?

The derivative of a{r}(xc,x) is (ac,(derivative of {r}(x)x+1*{r}(x)))

What is the first derivative of a{r}(xc,x) ?

The first derivative of a{r}(xc,x) is (ac,(derivative of {r}(x)x+1*{r}(x)))

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\frac{d}{d x} (a r (x) c, x)

(a c, (\frac{d}{d x} (r (x)) x + 1 \cdot r (x)))

Solution steps

\frac{d}{d x} (a r (x) c, x)

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= (a c, \frac{d}{d x} (r (x) x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = r (x), g = x

= (a c, (\frac{d}{d x} (r (x)) x + \frac{d x}{d x} r (x)))

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

= (a c, (\frac{d}{d x} (r (x)) x + 1 \cdot r (x)))

What is the derivative of a{r}(xc,x) ?
The derivative of a{r}(xc,x) is (ac,(derivative of {r}(x)x+1*{r}(x)))
What is the first derivative of a{r}(xc,x) ?
The first derivative of a{r}(xc,x) is (ac,(derivative of {r}(x)x+1*{r}(x)))