Solve -2/4x^3y^41/2x^2y^2

$$- \frac { 2 } { 4 } x ^ { 3 } y ^ { 4 } \frac { 1 } { 2 } x ^ { 2 } y ^ { 2 }$$

Evaluate

$$-\frac{x^{5}y^{6}}{4}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

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

Use the Commutative Property of Multiplication.

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

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

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

Add the exponents 3 and 2.

$$\left(-\frac{1}{2}\right)^{1}\times \left(\frac{1}{2}\right)^{1}x^{5}y^{4+2}$$

Add the exponents 4 and 2.

$$\left(-\frac{1}{2}\right)^{1}\times \left(\frac{1}{2}\right)^{1}x^{5}y^{6}$$

Multiply -\frac{1}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$-\frac{1}{4}x^{5}y^{6}$$

Differentiate w.r.t. x

$$-\frac{5x^{4}y^{6}}{4}$$