Solve 2v^3(-4v^6)

$$2 v ^ { 3 } ( - 4 v ^ { 6 } )$$

Evaluate

$$-8v^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$2v^{9}\left(-4\right)$$

Multiply 2 and -4 to get -8.

$$-8v^{9}$$

Differentiate w.r.t. v

$$-72v^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}v}(2v^{9}\left(-4\right))$$

Multiply 2 and -4 to get -8.

$$\frac{\mathrm{d}}{\mathrm{d}v}(-8v^{9})$$

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

$$9\left(-8\right)v^{9-1}$$

Multiply 9 times -8.

$$-72v^{9-1}$$

Subtract 1 from 9.

$$-72v^{8}$$