Solve frac{17x^{2}y}{5a^{3}c}*15a^2b/22xy^2*2xy^3/3ab^2

$$\frac { 17 x ^ { 2 } y } { 5 a ^ { 3 } c } \times \frac { 15 a ^ { 2 } b } { 22 x y ^ { 2 } } \times \frac { 2 x y ^ { 3 } } { 3 a b ^ { 2 } }$$

Evaluate

$$\frac{17\times \left(\frac{xy}{a}\right)^{2}}{11bc}$$

Solution Steps

Multiply \frac{17x^{2}y}{5a^{3}c} times \frac{15a^{2}b}{22xy^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17x^{2}y\times 15a^{2}b}{5a^{3}c\times 22xy^{2}}\times \frac{2xy^{3}}{3ab^{2}}$$

Cancel out 5xya^{2} in both numerator and denominator.

$$\frac{3\times 17bx}{22acy}\times \frac{2xy^{3}}{3ab^{2}}$$

Multiply \frac{3\times 17bx}{22acy} times \frac{2xy^{3}}{3ab^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 17bx\times 2xy^{3}}{22acy\times 3ab^{2}}$$

Cancel out 2\times 3by in both numerator and denominator.

$$\frac{17xxy^{2}}{11aabc}$$

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

$$\frac{17x^{2}y^{2}}{11aabc}$$

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

$$\frac{17x^{2}y^{2}}{11a^{2}bc}$$

Differentiate w.r.t. x

$$\frac{34\times \left(\frac{y}{a}\right)^{2}x}{11bc}$$