Solve {x}^frac{2{3}}*4x

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

Differentiate w.r.t. x

$$\frac{20x^{\frac{2}{3}}}{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{2}{3} and 1 to get \frac{5}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{5}{3}}\times 4)$$

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

$$\frac{5}{3}\times 4x^{\frac{5}{3}-1}$$

Multiply \frac{5}{3} times 4.

$$\frac{20}{3}x^{\frac{5}{3}-1}$$

Subtract 1 from \frac{5}{3}.

$$\frac{20}{3}x^{\frac{2}{3}}$$

Evaluate

$$4x^{\frac{5}{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{2}{3} and 1 to get \frac{5}{3}.

$$x^{\frac{5}{3}}\times 4$$