Solve frac{2x^{2}y}{x^{3}y^2}*4x^7y^2/2x^3

$$\frac { 2 x ^ { 2 } y } { x ^ { 3 } y ^ { 2 } } \cdot \frac { 4 x ^ { 7 } y ^ { 2 } } { 2 x ^ { 3 } }$$

Evaluate

$$4yx^{3}$$

Solution Steps

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

$$\frac{2}{xy}\times \frac{4x^{7}y^{2}}{2x^{3}}$$

Cancel out 2x^{3} in both numerator and denominator.

$$\frac{2}{xy}\times 2y^{2}x^{4}$$

Express \frac{2}{xy}\times 2 as a single fraction.

$$\frac{2\times 2}{xy}y^{2}x^{4}$$

Express \frac{2\times 2}{xy}y^{2} as a single fraction.

$$\frac{2\times 2y^{2}}{xy}x^{4}$$

Cancel out y in both numerator and denominator.

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

Express \frac{2\times 2y}{x}x^{4} as a single fraction.

$$\frac{2\times 2yx^{4}}{x}$$

Cancel out x in both numerator and denominator.

$$2\times 2yx^{3}$$

Multiply 2 and 2 to get 4.

$$4yx^{3}$$

Differentiate w.r.t. x

$$12yx^{2}$$