Solve -x^2y/4*20y^3/3

$$\frac { - x ^ { 2 } y } { 4 } \times \frac { 20 y ^ { 3 } } { 3 }$$

Evaluate

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

Solution Steps

Multiply \frac{\left(-x^{2}\right)y}{4} times \frac{20y^{3}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(-x^{2}\right)y\times 20y^{3}}{4\times 3}$$

Cancel out 4 in both numerator and denominator.

$$\frac{5y\left(-x^{2}\right)y^{3}}{3}$$

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

$$\frac{5y^{4}\left(-x^{2}\right)}{3}$$

Multiply 5 and -1 to get -5.

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

Differentiate w.r.t. x

$$-\frac{10xy^{4}}{3}$$