Solve a^5*a^3/-2

$$\frac { a ^ { 5 } \cdot a ^ { 3 } } { - 2 }$$

Differentiate w.r.t. a

$$-4a^{7}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{8}}{-2})$$

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

$$8\left(-\frac{1}{2}\right)a^{8-1}$$

Multiply 8 times -\frac{1}{2}.

$$-4a^{8-1}$$

Subtract 1 from 8.

$$-4a^{7}$$

Evaluate

$$-\frac{a^{8}}{2}$$

Solution Steps

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

$$\frac{a^{8}}{-2}$$