Solve (-5a^3/2)(2a^1/2)

$$( - 5 a ^ { 3 / 2 } ) ( 2 a ^ { 1 / 2 } )$$

Evaluate

$$-10a^{2}$$

Solution Steps

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

$$-5a^{2}\times 2$$

Multiply -5 and 2 to get -10.

$$-10a^{2}$$

Differentiate w.r.t. a

$$-20a$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(-5a^{2}\times 2)$$

Multiply -5 and 2 to get -10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-10a^{2})$$

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

$$2\left(-10\right)a^{2-1}$$

Multiply 2 times -10.

$$-20a^{2-1}$$

Subtract 1 from 2.

$$-20a^{1}$$

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

$$-20a$$