Solve c^12:c^2:c^2

$$c ^ { 12 } : c ^ { 2 } : c ^ { 2 }$$

Evaluate

$$c^{8}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 12 to get 10.

$$\frac{c^{10}}{c^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 10 to get 8.

$$c^{8}$$

Differentiate w.r.t. c

$$8c^{7}$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 12 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{c^{10}}{c^{2}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 10 to get 8.

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

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

$$8c^{8-1}$$

Subtract 1 from 8.

$$8c^{7}$$