Solve (2x^3)4x^frac{1{3}}

$$( 2 x ^ { 3 } ) 4 x ^ { \frac { 1 } { 3 } }$$

Evaluate

$$8x^{\frac{10}{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and \frac{1}{3} to get \frac{10}{3}.

$$2x^{\frac{10}{3}}\times 4$$

Multiply 2 and 4 to get 8.

$$8x^{\frac{10}{3}}$$

Differentiate w.r.t. x

$$\frac{80x^{\frac{7}{3}}}{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and \frac{1}{3} to get \frac{10}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{\frac{10}{3}}\times 4)$$

Multiply 2 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{\frac{10}{3}})$$

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

$$\frac{10}{3}\times 8x^{\frac{10}{3}-1}$$

Multiply \frac{10}{3} times 8.

$$\frac{80}{3}x^{\frac{10}{3}-1}$$

Subtract 1 from \frac{10}{3}.

$$\frac{80}{3}x^{\frac{7}{3}}$$