Solving: $\frac{d}{dx}\left(y\arctan\left(\frac{x}{2}\right)+\arctan\left(\frac{2}{x}\right)\right)$
Exercise
$\frac{dy}{dx}\left(yarctan\left(\frac{x}{2}\right)+arctan\left(\frac{2}{x}\right)\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Find the derivative d/dx(yarctan(x/2)+arctan(2/x)) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Taking the derivative of arctangent. Taking the derivative of arctangent.
Find the derivative d/dx(yarctan(x/2)+arctan(2/x)) using the sum rule
Final answer to the exercise
$\frac{y}{2\left(1+\left(\frac{x}{2}\right)^2\right)}+\frac{-2}{\left(1+\left(\frac{2}{x}\right)^2\right)x^2}$