Solve -4a^2*1/2a^3=

$$- 4 a ^ { 2 } * \frac { 1 } { 2 } a ^ { 3 } =$$

Evaluate

$$-2a^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$-4a^{5}\times \frac{1}{2}$$

Multiply -4 and \frac{1}{2} to get -2.

$$-2a^{5}$$

Differentiate w.r.t. a

$$-10a^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-4a^{5}\times \frac{1}{2})$$

Multiply -4 and \frac{1}{2} to get -2.

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

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

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

Multiply 5 times -2.

$$-10a^{5-1}$$

Subtract 1 from 5.

$$-10a^{4}$$