Solve frac{u^{4}v^4}{uv^4*2u^2v^4}

$$\frac { u ^ { 4 } v ^ { 4 } } { u v ^ { 4 } \cdot 2 u ^ { 2 } v ^ { 4 } }$$

Evaluate

$$\frac{u}{2v^{4}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{u^{4}v^{4}}{u^{3}v^{4}\times 2v^{4}}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{u^{4}v^{4}}{u^{3}v^{8}\times 2}$$

Cancel out u^{3}v^{4} in both numerator and denominator.

$$\frac{u}{2v^{4}}$$

Differentiate w.r.t. v

$$-\frac{2u}{v^{5}}$$