Solve 7(2/3*7/6)/5/frac{x(frac{92{3})}{2}}

$$\frac { \frac { 7 ( \frac { 2 } { 3 } \times \frac { 7 } { 6 } ) } { 5 } } { \frac { x ( \frac { 92 } { 3 } ) } { 2 } }$$

Evaluate

$$\frac{49}{690x}$$

Solution Steps

Divide \frac{7\times \frac{2}{3}\times \frac{7}{6}}{5} by \frac{x\times \frac{92}{3}}{2} by multiplying \frac{7\times \frac{2}{3}\times \frac{7}{6}}{5} by the reciprocal of \frac{x\times \frac{92}{3}}{2}.

$$\frac{7\times \frac{2}{3}\times \frac{7}{6}\times 2}{5x\times \frac{92}{3}}$$

Express 7\times \frac{2}{3} as a single fraction.

$$\frac{\frac{7\times 2}{3}\times \frac{7}{6}\times 2}{5x\times \frac{92}{3}}$$

Multiply 7 and 2 to get 14.

$$\frac{\frac{14}{3}\times \frac{7}{6}\times 2}{5x\times \frac{92}{3}}$$

Multiply \frac{14}{3} times \frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{14\times 7}{3\times 6}\times 2}{5x\times \frac{92}{3}}$$

Do the multiplications in the fraction \frac{14\times 7}{3\times 6}.

$$\frac{\frac{98}{18}\times 2}{5x\times \frac{92}{3}}$$

Reduce the fraction \frac{98}{18} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{49}{9}\times 2}{5x\times \frac{92}{3}}$$

Express \frac{49}{9}\times 2 as a single fraction.

$$\frac{\frac{49\times 2}{9}}{5x\times \frac{92}{3}}$$

Multiply 49 and 2 to get 98.

$$\frac{\frac{98}{9}}{5x\times \frac{92}{3}}$$

Express 5\times \frac{92}{3} as a single fraction.

$$\frac{\frac{98}{9}}{\frac{5\times 92}{3}x}$$

Multiply 5 and 92 to get 460.

$$\frac{\frac{98}{9}}{\frac{460}{3}x}$$

Express \frac{\frac{98}{9}}{\frac{460}{3}x} as a single fraction.

$$\frac{98}{9\times \frac{460}{3}x}$$

Express 9\times \frac{460}{3} as a single fraction.

$$\frac{98}{\frac{9\times 460}{3}x}$$

Multiply 9 and 460 to get 4140.

$$\frac{98}{\frac{4140}{3}x}$$

Divide 4140 by 3 to get 1380.

$$\frac{98}{1380x}$$

Differentiate w.r.t. x

$$-\frac{49}{690x^{2}}$$