Solve (frac{x^{4}z^{2}}{4y^3})(2x^3y^2/z^3)

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

Evaluate

$$\frac{x^{7}}{2yz}$$

Solution Steps

Multiply \frac{x^{4}z^{2}}{4y^{3}} times \frac{2x^{3}y^{2}}{z^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{4}z^{2}\times 2x^{3}y^{2}}{4y^{3}z^{3}}$$

Cancel out 2y^{2}z^{2} in both numerator and denominator.

$$\frac{x^{3}x^{4}}{2yz}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{x^{7}}{2yz}$$

Differentiate w.r.t. x

$$\frac{7x^{6}}{2yz}$$