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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = r (x), g = ln (x)

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

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

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

\int x (x^{2} - 2) d x

\frac{1}{4 x ^{2} + 5 x}

f (x) = 8 x^{2} - x^{3}, (1, 7)

(x - 5)^{\frac{7}{3}}

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