Solve 8c^3quad2c^2

$$8 c ^ { 3 } \quad 2 c ^ { 2 }$$

Evaluate

$$16c^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$8c^{5}\times 2$$

Multiply 8 and 2 to get 16.

$$16c^{5}$$

Differentiate w.r.t. c

$$80c^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}c}(8c^{5}\times 2)$$

Multiply 8 and 2 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}c}(16c^{5})$$

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

$$5\times 16c^{5-1}$$

Multiply 5 times 16.

$$80c^{5-1}$$

Subtract 1 from 5.

$$80c^{4}$$