Solve -a^3*a*a^4

$$- a ^ { 3 } \cdot a \cdot a ^ { 4 }$$

Evaluate

$$-a^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

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

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$-a^{8}$$

Differentiate w.r.t. a

$$-8a^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

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

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

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

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

$$8\left(-1\right)a^{8-1}$$

Multiply 8 times -1.

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

Subtract 1 from 8.

$$-8a^{7}$$