Solve c^9*c*c^4*c^21

$$c ^ { 9 } \cdot c \cdot c ^ { 4 } \cdot c ^ { 21 }$$

Evaluate

$$c^{35}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and 1 to get 10.

$$c^{10}c^{4}c^{21}$$

To multiply powers of the same base, add their exponents. Add 10 and 4 to get 14.

$$c^{14}c^{21}$$

To multiply powers of the same base, add their exponents. Add 14 and 21 to get 35.

$$c^{35}$$

Differentiate w.r.t. c

$$35c^{34}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 9 and 1 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c^{10}c^{4}c^{21})$$

To multiply powers of the same base, add their exponents. Add 10 and 4 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c^{14}c^{21})$$

To multiply powers of the same base, add their exponents. Add 14 and 21 to get 35.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c^{35})$$

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

$$35c^{35-1}$$

Subtract 1 from 35.

$$35c^{34}$$