Solve -5v^4*2v^3

$$- 5 v ^ { 4 } \cdot 2 v ^ { 3 }$$

Evaluate

$$-10v^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$-5v^{7}\times 2$$

Multiply -5 and 2 to get -10.

$$-10v^{7}$$

Differentiate w.r.t. v

$$-70v^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}v}(-5v^{7}\times 2)$$

Multiply -5 and 2 to get -10.

$$\frac{\mathrm{d}}{\mathrm{d}v}(-10v^{7})$$

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

$$7\left(-10\right)v^{7-1}$$

Multiply 7 times -10.

$$-70v^{7-1}$$

Subtract 1 from 7.

$$-70v^{6}$$