Solve 1/2xy^2*(-4x^3y)*(-6y^3)

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

Evaluate

$$12x^{4}y^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

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

Multiply \frac{1}{2} and -4 to get -2.

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

Multiply -2 and -6 to get 12.

$$12x^{4}y^{6}$$

Differentiate w.r.t. x

$$48x^{3}y^{6}$$