Solve 20c^8:5c^5=

$$20 c ^ { 8 } : 5 c ^ { 5 } =$$

Evaluate

$$4c^{13}$$

Solution Steps

Divide 20c^{8} by 5 to get 4c^{8}.

$$4c^{8}c^{5}$$

To multiply powers of the same base, add their exponents. Add 8 and 5 to get 13.

$$4c^{13}$$

Differentiate w.r.t. c

$$52c^{12}$$

Steps Using Definition of a Derivative

Divide 20c^{8} by 5 to get 4c^{8}.

$$\frac{\mathrm{d}}{\mathrm{d}c}(4c^{8}c^{5})$$

To multiply powers of the same base, add their exponents. Add 8 and 5 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}c}(4c^{13})$$

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

$$13\times 4c^{13-1}$$

Multiply 13 times 4.

$$52c^{13-1}$$

Subtract 1 from 13.

$$52c^{12}$$