Solve frac{x^frac{3{2}}}{2x^-frac{1{8}}}=

$$\frac { x ^ { \frac { 3 } { 2 } } } { 2 x ^ { - \frac { 1 } { 8 } } } =$$

Differentiate w.r.t. x

$$\frac{13x^{\frac{5}{8}}}{16}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{\frac{3}{2}-\left(-\frac{1}{8}\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{\frac{13}{8}})$$

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}.

$$\frac{13}{8}\times \frac{1}{2}x^{\frac{13}{8}-1}$$

Do the arithmetic.

$$\frac{13}{16}x^{\frac{5}{8}}$$

Evaluate

$$\frac{x^{\frac{13}{8}}}{2}$$