Solve frac{-12t^{-1}u^5v^-4}{2t^-3uv^5}

$$\frac { - 12 t ^ { - 1 } u ^ { 5 } v ^ { - 4 } } { 2 t ^ { - 3 } u v ^ { 5 } }$$

Evaluate

$$-\frac{6t^{2}u^{4}}{v^{9}}$$

Solution Steps

Cancel out 2u in both numerator and denominator.

$$\frac{-6v^{-4}\times \frac{1}{t}u^{4}}{t^{-3}v^{5}}$$

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

$$\frac{-6v^{-4}t^{2}u^{4}}{v^{5}}$$

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

$$\frac{-6t^{2}u^{4}}{v^{9}}$$

Differentiate w.r.t. u

$$-\frac{24t^{2}u^{3}}{v^{9}}$$