Solve (-3c^3)(7c^-2)

$$( - 3 c ^ { 3 } ) ( 7 c ^ { - 2 } )$$

Evaluate

$$-21c$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.

$$-3c^{1}\times 7$$

Calculate c to the power of 1 and get c.

$$-3c\times 7$$

Multiply -3 and 7 to get -21.

$$-21c$$

Differentiate w.r.t. c

$$-21$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}c}(-3c^{1}\times 7)$$

Calculate c to the power of 1 and get c.

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

Multiply -3 and 7 to get -21.

$$\frac{\mathrm{d}}{\mathrm{d}c}(-21c)$$

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

$$-21c^{1-1}$$

Subtract 1 from 1.

$$-21c^{0}$$

For any term t except 0, t^{0}=1.

$$-21$$