Solve -2v^9*7v

$$- 2 v ^ { 9 } \cdot 7 v$$

Evaluate

$$-14v^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and 1 to get 10.

$$-2v^{10}\times 7$$

Multiply -2 and 7 to get -14.

$$-14v^{10}$$

Differentiate w.r.t. v

$$-140v^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 9 and 1 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}v}(-2v^{10}\times 7)$$

Multiply -2 and 7 to get -14.

$$\frac{\mathrm{d}}{\mathrm{d}v}(-14v^{10})$$

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

$$10\left(-14\right)v^{10-1}$$

Multiply 10 times -14.

$$-140v^{10-1}$$

Subtract 1 from 10.

$$-140v^{9}$$