Solve frac{35xy^{3}}{24x^3y}div15x^4y^3/84xy^4

$$\frac { 35 x y ^ { 3 } } { 24 x ^ { 3 } y } \div \frac { 15 x ^ { 4 } y ^ { 3 } } { 84 x y ^ { 4 } }$$

Evaluate

$$\frac{49y^{3}}{6x^{5}}$$

Solution Steps

Divide \frac{35xy^{3}}{24x^{3}y} by \frac{15x^{4}y^{3}}{84xy^{4}} by multiplying \frac{35xy^{3}}{24x^{3}y} by the reciprocal of \frac{15x^{4}y^{3}}{84xy^{4}}.

$$\frac{35xy^{3}\times 84xy^{4}}{24x^{3}y\times 15x^{4}y^{3}}$$

Cancel out 5\times 12xxyyy^{2} in both numerator and denominator.

$$\frac{7\times 7y^{3}}{2\times 3xx^{4}}$$

Multiply 7 and 7 to get 49.

$$\frac{49y^{3}}{2\times 3xx^{4}}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{49y^{3}}{2\times 3x^{5}}$$

Multiply 2 and 3 to get 6.

$$\frac{49y^{3}}{6x^{5}}$$

Differentiate w.r.t. x

$$-\frac{245y^{3}}{6x^{6}}$$