Solve (4uv)(-u)(2u^4v)

$$( 4 u v ) ( - u ) ( 2 u ^ { 4 } v )$$

Evaluate

$$-8v^{2}u^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$4u^{5}v\left(-u\right)\times 2v$$

Multiply v and v to get v^{2}.

$$4u^{5}v^{2}\left(-u\right)\times 2$$

Multiply 4 and 2 to get 8.

$$8u^{5}v^{2}\left(-u\right)$$

Multiply 8 and -1 to get -8.

$$-8u^{5}v^{2}u$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$-8u^{6}v^{2}$$

Differentiate w.r.t. v

$$-16vu^{6}$$