Solve 2/3x(-3xy)(-y^2)+4xy^2(-xy)+(-3y^3)(-2x^2)

$$\frac { 2 } { 3 } x ( - 3 x y ) ( - y ^ { 2 } ) + 4 x y ^ { 2 } ( - x y ) + ( - 3 y ^ { 3 } ) ( - 2 x ^ { 2 } )$$

Evaluate

$$4x^{2}y^{3}$$

Solution Steps

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

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

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

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

Multiply \frac{2}{3} and -3 to get -2.

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

Multiply -2 and -1 to get 2.

$$2x^{2}yy^{2}+4xy^{3}\left(-x\right)-3y^{3}\left(-2\right)x^{2}$$

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

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

Multiply -3 and -2 to get 6.

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

Combine 2x^{2}y^{3} and 6y^{3}x^{2} to get 8x^{2}y^{3}.

$$8x^{2}y^{3}+4xy^{3}\left(-x\right)$$

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

$$8x^{2}y^{3}+4x^{2}y^{3}\left(-1\right)$$

Multiply 4 and -1 to get -4.

$$8x^{2}y^{3}-4x^{2}y^{3}$$

Combine 8x^{2}y^{3} and -4x^{2}y^{3} to get 4x^{2}y^{3}.

$$4x^{2}y^{3}$$

Differentiate w.r.t. x

$$8xy^{3}$$