Solve (x^{3}y)(xy^2z^2)(y^3z^2)=

$$( x ^ { 3 } y ) ( x y ^ { 2 } z ^ { 2 } ) ( y ^ { 3 } z ^ { 2 } ) =$$

Evaluate

$$y^{6}\left(xz\right)^{4}$$

Solution Steps

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

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

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

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

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

$$x^{4}y^{6}z^{2}z^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

Differentiate w.r.t. x

$$4x^{3}z^{4}y^{6}$$