Solve c^6c^9c^10c^32

$$c ^ { 6 } c ^ { 9 } c ^ { 10 } c ^ { 32 }$$

Evaluate

$$c^{57}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 9 to get 15.

$$c^{15}c^{10}c^{32}$$

To multiply powers of the same base, add their exponents. Add 15 and 10 to get 25.

$$c^{25}c^{32}$$

To multiply powers of the same base, add their exponents. Add 25 and 32 to get 57.

$$c^{57}$$

Differentiate w.r.t. c

$$57c^{56}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 9 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c^{15}c^{10}c^{32})$$

To multiply powers of the same base, add their exponents. Add 15 and 10 to get 25.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c^{25}c^{32})$$

To multiply powers of the same base, add their exponents. Add 25 and 32 to get 57.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c^{57})$$

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

$$57c^{57-1}$$

Subtract 1 from 57.

$$57c^{56}$$