Solve 25c^215c

$$25 c ^ { 2 } 15 c$$

Evaluate

$$375c^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$25c^{3}\times 15$$

Multiply 25 and 15 to get 375.

$$375c^{3}$$

Differentiate w.r.t. c

$$1125c^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}c}(25c^{3}\times 15)$$

Multiply 25 and 15 to get 375.

$$\frac{\mathrm{d}}{\mathrm{d}c}(375c^{3})$$

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

$$3\times 375c^{3-1}$$

Multiply 3 times 375.

$$1125c^{3-1}$$

Subtract 1 from 3.

$$1125c^{2}$$