Solve 4x^2y^3*2xydivx^5y^3

$$4 x ^ { 2 } y ^ { 3 } \times 2 x y \div x ^ { 5 } y ^ { 3 }$$

Evaluate

$$\frac{8y^{7}}{x^{2}}$$

Solution Steps

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

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

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

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

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

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

Multiply 2 and 4 to get 8.

$$\frac{8y^{4}}{x^{2}}y^{3}$$

Express \frac{8y^{4}}{x^{2}}y^{3} as a single fraction.

$$\frac{8y^{4}y^{3}}{x^{2}}$$

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

$$\frac{8y^{7}}{x^{2}}$$

Differentiate w.r.t. x

$$-\frac{16y^{7}}{x^{3}}$$