Solve 2x^3y/3z^4*6xz^5/10y^5

$$\frac { 2 x ^ { 3 } y } { 3 z ^ { 4 } } \cdot \frac { 6 x z ^ { 5 } } { 10 y ^ { 5 } }$$

Evaluate

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

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{2x^{3}y}{3z^{4}}\times \frac{3xz^{5}}{5y^{5}}$$

Multiply \frac{2x^{3}y}{3z^{4}} times \frac{3xz^{5}}{5y^{5}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2x^{3}y\times 3xz^{5}}{3z^{4}\times 5y^{5}}$$

Cancel out 3yz^{4} in both numerator and denominator.

$$\frac{2xzx^{3}}{5y^{4}}$$

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

$$\frac{2x^{4}z}{5y^{4}}$$

Differentiate w.r.t. x

$$\frac{8zx^{3}}{5y^{4}}$$