Solve 28x^5/7x^16*14y^7/16x^2

$$\frac { 28 x ^ { 5 } } { 7 x ^ { 16 } } \cdot \frac { 14 y ^ { 7 } } { 16 x ^ { 2 } }$$

Evaluate

$$\frac{7y^{7}}{2x^{13}}$$

Solution Steps

Cancel out 7x^{5} in both numerator and denominator.

$$\frac{4}{x^{11}}\times \frac{14y^{7}}{16x^{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{4}{x^{11}}\times \frac{7y^{7}}{8x^{2}}$$

Multiply \frac{4}{x^{11}} times \frac{7y^{7}}{8x^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 7y^{7}}{x^{11}\times 8x^{2}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{7y^{7}}{2x^{2}x^{11}}$$

To multiply powers of the same base, add their exponents. Add 2 and 11 to get 13.

$$\frac{7y^{7}}{2x^{13}}$$

Differentiate w.r.t. x

$$-\frac{91y^{7}}{2x^{14}}$$