Solve x^frac{1{2}}x^frac{2{3}}quad15

$$x ^ { \frac { 1 } { 2 } } x ^ { \frac { 2 } { 3 } } \quad 15$$

Differentiate w.r.t. x

$$\frac{35\sqrt[6]{x}}{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{1}{2} and \frac{2}{3} to get \frac{7}{6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{7}{6}}\times 15)$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{7}{6}\times 15x^{\frac{7}{6}-1}$$

Multiply \frac{7}{6} times 15.

$$\frac{35}{2}x^{\frac{7}{6}-1}$$

Subtract 1 from \frac{7}{6}.

$$\frac{35}{2}\sqrt[6]{x}$$

Evaluate

$$15x^{\frac{7}{6}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{1}{2} and \frac{2}{3} to get \frac{7}{6}.

$$x^{\frac{7}{6}}\times 15$$