Solve xy^9/3y^-2*-7y/21x^5

$$\frac { x y ^ { 9 } } { 3 y ^ { - 2 } } \cdot \frac { - 7 y } { 21 x ^ { 5 } }$$

Evaluate

$$-\frac{y^{12}}{9x^{4}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{xy^{11}}{3}\times \frac{-7y}{21x^{5}}$$

Cancel out 7 in both numerator and denominator.

$$\frac{xy^{11}}{3}\times \frac{-y}{3x^{5}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{xy^{11}}{3}\times \frac{y}{-3x^{5}}$$

Multiply \frac{xy^{11}}{3} times \frac{y}{-3x^{5}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{xy^{11}y}{3\left(-3\right)x^{5}}$$

Cancel out x in both numerator and denominator.

$$\frac{yy^{11}}{-3\times 3x^{4}}$$

To multiply powers of the same base, add their exponents. Add 1 and 11 to get 12.

$$\frac{y^{12}}{-3\times 3x^{4}}$$

Multiply -3 and 3 to get -9.

$$\frac{y^{12}}{-9x^{4}}$$

Differentiate w.r.t. x

$$\frac{4y^{12}}{9x^{5}}$$