Solve 3xy^3:4xy^2*1/2x

$$3 x y ^ { 3 } : 4 x y ^ { 2 } \cdot \frac { 1 } { 2 } x$$

Evaluate

$$\frac{3x^{3}y^{5}}{8}$$

Solution Steps

Multiply x and x to get x^{2}.

$$\frac{3xy^{3}}{4}x^{2}y^{2}\times \frac{1}{2}$$

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

$$\frac{3xy^{3}x^{2}}{4}y^{2}\times \frac{1}{2}$$

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

$$\frac{3xy^{3}x^{2}y^{2}}{4}\times \frac{1}{2}$$

Multiply \frac{3xy^{3}x^{2}y^{2}}{4} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

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

Multiply 4 and 2 to get 8.

$$\frac{3x^{3}y^{5}}{8}$$

Differentiate w.r.t. x

$$\frac{9x^{2}y^{5}}{8}$$