Solve (-2x^frac{1{3}})(-5x^frac{2{3}})

$$( - 2 x ^ { \frac { 1 } { 3 } } ) ( - 5 x ^ { \frac { 2 } { 3 } } )$$

Evaluate

$$10x$$

Solution Steps

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

$$-2x^{1}\left(-5\right)$$

Calculate x to the power of 1 and get x.

$$-2x\left(-5\right)$$

Multiply -2 and -5 to get 10.

$$10x$$

Differentiate w.r.t. x

$$10$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{1}\left(-5\right))$$

Calculate x to the power of 1 and get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x\left(-5\right))$$

Multiply -2 and -5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x)$$

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

$$10x^{1-1}$$

Subtract 1 from 1.

$$10x^{0}$$

For any term t except 0, t^{0}=1.

$$10\times 1$$

For any term t, t\times 1=t and 1t=t.

$$10$$