Exercise
$\frac{d}{dx}\left(\frac{\sin\left(5x\right)+\cos\left(5x\right)}{\sin\left(5x\right)-\cos\left(5x\right)}\right)^3$
Step-by-step Solution
Final answer to the exercise
$\left(\frac{\sin\left(5x\right)+\cos\left(5x\right)}{\sin\left(5x\right)-\cos\left(5x\right)}\right)^{2}\frac{3\left(\left(5\cos\left(5x\right)-5\sin\left(5x\right)\right)\left(\sin\left(5x\right)-\cos\left(5x\right)\right)+\left(-\sin\left(5x\right)-\cos\left(5x\right)\right)\left(5\cos\left(5x\right)+5\sin\left(5x\right)\right)\right)}{\left(\sin\left(5x\right)-\cos\left(5x\right)\right)^2}$