Solve x/yz^2*y/x^2*7z/x^2

$$\frac { x } { y z ^ { 2 } } \cdot \frac { y } { x ^ { 2 } } \times \frac { 7 z } { x ^ { 2 } }$$

Evaluate

$$\frac{7}{zx^{3}}$$

Solution Steps

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

$$\frac{xy}{yz^{2}x^{2}}\times \frac{7z}{x^{2}}$$

Cancel out xy in both numerator and denominator.

$$\frac{1}{xz^{2}}\times \frac{7z}{x^{2}}$$

Multiply \frac{1}{xz^{2}} times \frac{7z}{x^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7z}{xz^{2}x^{2}}$$

Cancel out z in both numerator and denominator.

$$\frac{7}{xzx^{2}}$$

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

$$\frac{7}{x^{3}z}$$

Differentiate w.r.t. x

$$-\frac{21}{zx^{4}}$$