Solve (-a)(-a^3)(-a^5)

$$( - a ) ( - a ^ { 3 } ) ( - a ^ { 5 } )$$

Evaluate

$$-a^{9}$$

Solution Steps

Multiply -1 and -1 to get 1.

$$aa^{3}\left(-1\right)a^{5}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$a^{4}\left(-1\right)a^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$a^{9}\left(-1\right)$$

Differentiate w.r.t. a

$$-9a^{8}$$

Steps Using Definition of a Derivative

Multiply -1 and -1 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(aa^{3}\left(-1\right)a^{5})$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{4}\left(-1\right)a^{5})$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{9}\left(-1\right))$$

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

$$9\left(-1\right)a^{9-1}$$

Multiply 9 times -1.

$$-9a^{9-1}$$

Subtract 1 from 9.

$$-9a^{8}$$