Solve 2/5x^2y^3*5/16xyz*(-2x^2y)

$$\frac { 2 } { 5 } x ^ { 2 } y ^ { 3 } \cdot \frac { 5 } { 16 } x y z \cdot ( - 2 x ^ { 2 } y )$$

Evaluate

$$-\frac{z\left(xy\right)^{5}}{4}$$

Solution Steps

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

$$\frac{2}{5}x^{3}y^{3}\times \frac{5}{16}yz\left(-2\right)x^{2}y$$

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

$$\frac{2}{5}x^{5}y^{3}\times \frac{5}{16}yz\left(-2\right)y$$

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

$$\frac{2}{5}x^{5}y^{4}\times \frac{5}{16}z\left(-2\right)y$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{2}{5}x^{5}y^{5}\times \frac{5}{16}z\left(-2\right)$$

Multiply \frac{2}{5} and \frac{5}{16} to get \frac{1}{8}.

$$\frac{1}{8}x^{5}y^{5}z\left(-2\right)$$

Multiply \frac{1}{8} and -2 to get -\frac{1}{4}.

$$-\frac{1}{4}x^{5}y^{5}z$$

Differentiate w.r.t. x

$$-\frac{5zx^{4}y^{5}}{4}$$