Solve 1/5xy^{3}(15/2xy)+3/8x^{2}y(4/21y^3)-frac{1}{7}y^2(frac{35}{2}x^2y^2)

$$\frac { 1 } { 5 } x y ^ { 3 } ( \frac { 15 } { 2 } x y ) + \frac { 3 } { 8 } x ^ { 2 } y ( \frac { 4 } { 21 } y ^ { 3 } ) - \frac { 1 } { 7 } y ^ { 2 } ( \frac { 35 } { 2 } x ^ { 2 } y ^ { 2 } )$$

Evaluate

$$-\frac{13x^{2}y^{4}}{14}$$

Solution Steps

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

$$\frac{1}{5}x^{2}y^{3}\times \frac{15}{2}y+\frac{3}{8}x^{2}y\times \frac{4}{21}y^{3}-\frac{1}{7}y^{2}\times \frac{35}{2}x^{2}y^{2}$$

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

$$\frac{1}{5}x^{2}y^{4}\times \frac{15}{2}+\frac{3}{8}x^{2}y\times \frac{4}{21}y^{3}-\frac{1}{7}y^{2}\times \frac{35}{2}x^{2}y^{2}$$

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

$$\frac{1}{5}x^{2}y^{4}\times \frac{15}{2}+\frac{3}{8}x^{2}y^{4}\times \frac{4}{21}-\frac{1}{7}y^{2}\times \frac{35}{2}x^{2}y^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{1}{5}x^{2}y^{4}\times \frac{15}{2}+\frac{3}{8}x^{2}y^{4}\times \frac{4}{21}-\frac{1}{7}y^{4}\times \frac{35}{2}x^{2}$$

Multiply \frac{1}{5} and \frac{15}{2} to get \frac{3}{2}.

$$\frac{3}{2}x^{2}y^{4}+\frac{3}{8}x^{2}y^{4}\times \frac{4}{21}-\frac{1}{7}y^{4}\times \frac{35}{2}x^{2}$$

Multiply \frac{3}{8} and \frac{4}{21} to get \frac{1}{14}.

$$\frac{3}{2}x^{2}y^{4}+\frac{1}{14}x^{2}y^{4}-\frac{1}{7}y^{4}\times \frac{35}{2}x^{2}$$

Combine \frac{3}{2}x^{2}y^{4} and \frac{1}{14}x^{2}y^{4} to get \frac{11}{7}x^{2}y^{4}.

$$\frac{11}{7}x^{2}y^{4}-\frac{1}{7}y^{4}\times \frac{35}{2}x^{2}$$

Multiply \frac{1}{7} and \frac{35}{2} to get \frac{5}{2}.

$$\frac{11}{7}x^{2}y^{4}-\frac{5}{2}y^{4}x^{2}$$

Combine \frac{11}{7}x^{2}y^{4} and -\frac{5}{2}y^{4}x^{2} to get -\frac{13}{14}x^{2}y^{4}.

$$-\frac{13}{14}x^{2}y^{4}$$

Differentiate w.r.t. x

$$-\frac{13xy^{4}}{7}$$