Solve -4x^2y*(-1/2x^4y^2)

$$- 4 x ^ { 2 } y \cdot ( - \frac { 1 } { 2 } x ^ { 4 } y ^ { 2 } )$$

Evaluate

$$2y^{3}x^{6}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-4\right)^{1}x^{2}y^{1}\left(-\frac{1}{2}\right)^{1}x^{4}y^{2}$$

Use the Commutative Property of Multiplication.

$$\left(-4\right)^{1}\left(-\frac{1}{2}\right)^{1}x^{2}x^{4}y^{1}y^{2}$$

To multiply powers of the same base, add their exponents.

$$\left(-4\right)^{1}\left(-\frac{1}{2}\right)^{1}x^{2+4}y^{1+2}$$

Add the exponents 2 and 4.

$$\left(-4\right)^{1}\left(-\frac{1}{2}\right)^{1}x^{6}y^{1+2}$$

Add the exponents 1 and 2.

$$\left(-4\right)^{1}\left(-\frac{1}{2}\right)^{1}x^{6}y^{3}$$

Multiply -4 times -\frac{1}{2}.

$$2x^{6}y^{3}$$

Differentiate w.r.t. x

$$12y^{3}x^{5}$$