Solve frac{frac{36x^{4}}{5y^4z^5}}{9xy^2/15z^5}

$$\frac { \frac { 36 x ^ { 4 } } { 5 y ^ { 4 } z ^ { 5 } } } { \frac { 9 x y ^ { 2 } } { 15 z ^ { 5 } } }$$

Evaluate

$$\frac{12x^{3}}{y^{6}}$$

Solution Steps

Divide \frac{36x^{4}}{5y^{4}z^{5}} by \frac{9xy^{2}}{15z^{5}} by multiplying \frac{36x^{4}}{5y^{4}z^{5}} by the reciprocal of \frac{9xy^{2}}{15z^{5}}.

$$\frac{36x^{4}\times 15z^{5}}{5y^{4}z^{5}\times 9xy^{2}}$$

Cancel out 5\times 9xz^{5} in both numerator and denominator.

$$\frac{3\times 4x^{3}}{y^{2}y^{4}}$$

Multiply 3 and 4 to get 12.

$$\frac{12x^{3}}{y^{2}y^{4}}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{12x^{3}}{y^{6}}$$

Differentiate w.r.t. x

$$\frac{36x^{2}}{y^{6}}$$