Solve (4a^10)(-6a^4)a

$$( 4 a ^ { 10 } ) ( - 6 a ^ { 4 } ) a$$

Evaluate

$$-24a^{15}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 10 and 4 to get 14.

$$4a^{14}\left(-6\right)a$$

To multiply powers of the same base, add their exponents. Add 14 and 1 to get 15.

$$4a^{15}\left(-6\right)$$

Multiply 4 and -6 to get -24.

$$-24a^{15}$$

Differentiate w.r.t. a

$$-360a^{14}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 10 and 4 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{14}\left(-6\right)a)$$

To multiply powers of the same base, add their exponents. Add 14 and 1 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{15}\left(-6\right))$$

Multiply 4 and -6 to get -24.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-24a^{15})$$

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

$$15\left(-24\right)a^{15-1}$$

Multiply 15 times -24.

$$-360a^{15-1}$$

Subtract 1 from 15.

$$-360a^{14}$$