Solve 5c^4*5c^1

$$5 c ^ { 4 } \times 5 c ^ { 1 }$$

Evaluate

$$25c^{5}$$

Solution Steps

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

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

Multiply 5 and 5 to get 25.

$$25c^{5}$$

Differentiate w.r.t. c

$$125c^{4}$$

Steps Using Definition of a Derivative

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

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

Multiply 5 and 5 to get 25.

$$\frac{\mathrm{d}}{\mathrm{d}c}(25c^{5})$$

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

$$5\times 25c^{5-1}$$

Multiply 5 times 25.

$$125c^{5-1}$$

Subtract 1 from 5.

$$125c^{4}$$