Exercise
$\frac{d}{dx}\:x\:csc\:y-\:cot\:x=x^2y$
Step-by-step Solution
Learn how to solve trigonometric identities problems step by step online. Find the implicit derivative d/dx(xcsc(y)-cot(x)=x^2y). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^2 and g=y. The derivative of the linear function is equal to 1. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.
Find the implicit derivative d/dx(xcsc(y)-cot(x)=x^2y)
Final answer to the exercise
$y^{\prime}=\frac{-2xy+\csc\left(y\right)+\csc\left(x\right)^2}{x\left(\csc\left(y\right)\cot\left(y\right)+x\right)}$