Solve r^2/4r^frac{1{2}}

$$\frac { r ^ { 2 } } { 4 r ^ { \frac { 1 } { 2 } } }$$

Differentiate w.r.t. r

$$\frac{3\sqrt{r}}{8}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{1}{4}r^{2-\frac{1}{2}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{1}{4}r^{\frac{3}{2}})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$\frac{3}{2}\times \frac{1}{4}r^{\frac{3}{2}-1}$$

Do the arithmetic.

$$\frac{3}{8}\sqrt{r}$$

Evaluate

$$\frac{r^{\frac{3}{2}}}{4}$$