Solve (c^5)^3c^4

$$( c ^ { 5 } ) ^ { 3 } c ^ { 4 }$$

Evaluate

$$c^{19}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$c^{15}c^{4}$$

To multiply powers of the same base, add their exponents. Add 15 and 4 to get 19.

$$c^{19}$$

Differentiate w.r.t. c

$$19c^{18}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c^{15}c^{4})$$

To multiply powers of the same base, add their exponents. Add 15 and 4 to get 19.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c^{19})$$

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

$$19c^{19-1}$$

Subtract 1 from 19.

$$19c^{18}$$