Solve -10x^2(-1/5xy^3)(+5/6x^3y^4)(-2/3xy)

$$- 10 x ^ { 2 } ( - \frac { 1 } { 5 } x y ^ { 3 } ) ( + \frac { 5 } { 6 } x ^ { 3 } y ^ { 4 } ) ( - \frac { 2 } { 3 } x y )$$

Evaluate

$$-\frac{10x^{7}y^{8}}{9}$$

Solution Steps

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

$$-10x^{3}\left(-\frac{1}{5}\right)y^{3}\times \frac{5}{6}x^{3}y^{4}\left(-\frac{2}{3}\right)xy$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$-10x^{6}\left(-\frac{1}{5}\right)y^{3}\times \frac{5}{6}y^{4}\left(-\frac{2}{3}\right)xy$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$-10x^{7}\left(-\frac{1}{5}\right)y^{3}\times \frac{5}{6}y^{4}\left(-\frac{2}{3}\right)y$$

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

$$-10x^{7}\left(-\frac{1}{5}\right)y^{7}\times \frac{5}{6}\left(-\frac{2}{3}\right)y$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$-10x^{7}\left(-\frac{1}{5}\right)y^{8}\times \frac{5}{6}\left(-\frac{2}{3}\right)$$

Multiply -10 and -\frac{1}{5} to get 2.

$$2x^{7}y^{8}\times \frac{5}{6}\left(-\frac{2}{3}\right)$$

Multiply 2 and \frac{5}{6} to get \frac{5}{3}.

$$\frac{5}{3}x^{7}y^{8}\left(-\frac{2}{3}\right)$$

Multiply \frac{5}{3} and -\frac{2}{3} to get -\frac{10}{9}.

$$-\frac{10}{9}x^{7}y^{8}$$

Differentiate w.r.t. x

$$-\frac{70x^{6}y^{8}}{9}$$