Solve c^5*c^2/c^3

$$\frac { c ^ { 5 } \times c ^ { 2 } } { c ^ { 3 } }$$

Evaluate

$$c^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{c^{7}}{c^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 7 to get 4.

$$c^{4}$$

Differentiate w.r.t. c

$$4c^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{c^{7}}{c^{3}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 7 to get 4.

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

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

$$4c^{4-1}$$

Subtract 1 from 4.

$$4c^{3}$$