Solve 6x^frac{2{3}}*2x^frac{1{2}}

$$6 x ^ { \frac { 2 } { 3 } } * 2 x ^ { \frac { 1 } { 2 } }$$

Evaluate

$$12x^{\frac{7}{6}}$$

Solution Steps

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

$$6x^{\frac{7}{6}}\times 2$$

Multiply 6 and 2 to get 12.

$$12x^{\frac{7}{6}}$$

Differentiate w.r.t. x

$$14\sqrt[6]{x}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{\frac{7}{6}}\times 2)$$

Multiply 6 and 2 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{\frac{7}{6}})$$

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

$$\frac{7}{6}\times 12x^{\frac{7}{6}-1}$$

Multiply \frac{7}{6} times 12.

$$14x^{\frac{7}{6}-1}$$

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

$$14\sqrt[6]{x}$$