Solve (2x^frac{1{5}})(6x^frac{1{4}})

$$( 2 x ^ { \frac { 1 } { 5 } } ) ( 6 x ^ { \frac { 1 } { 4 } } )$$

Evaluate

$$12x^{\frac{9}{20}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{1}{5} and \frac{1}{4} to get \frac{9}{20}.

$$2x^{\frac{9}{20}}\times 6$$

Multiply 2 and 6 to get 12.

$$12x^{\frac{9}{20}}$$

Differentiate w.r.t. x

$$\frac{27}{5x^{\frac{11}{20}}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{1}{5} and \frac{1}{4} to get \frac{9}{20}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{\frac{9}{20}}\times 6)$$

Multiply 2 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{\frac{9}{20}})$$

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

$$\frac{9}{20}\times 12x^{\frac{9}{20}-1}$$

Multiply \frac{9}{20} times 12.

$$\frac{27}{5}x^{\frac{9}{20}-1}$$

Subtract 1 from \frac{9}{20}.

$$\frac{27}{5}x^{-\frac{11}{20}}$$