Solve 2a^5(-a^2)(-5a)

$$2 a ^ { 5 } ( - a ^ { 2 } ) ( - 5 a )$$

Evaluate

$$10a^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$2a^{6}\left(-a^{2}\right)\left(-5\right)$$

Multiply 2 and -5 to get -10.

$$-10a^{6}\left(-a^{2}\right)$$

Multiply -10 and -1 to get 10.

$$10a^{6}a^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$10a^{8}$$

Differentiate w.r.t. a

$$80a^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{6}\left(-a^{2}\right)\left(-5\right))$$

Multiply 2 and -5 to get -10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-10a^{6}\left(-a^{2}\right))$$

Multiply -10 and -1 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(10a^{6}a^{2})$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}a}(10a^{8})$$

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

$$8\times 10a^{8-1}$$

Multiply 8 times 10.

$$80a^{8-1}$$

Subtract 1 from 8.

$$80a^{7}$$