Find the derivative $\frac{d}{dx}\left(\ln\left(\frac{1+\sqrt{\sin\left(x\right)}}{1-\sqrt{\sin\left(x\right)}}\right)+2\arctan\left(\sqrt{\sin\left(x\right)}\right)\right)$ using the sum rule

Got another answer? Verify it here!

Learn how to solve sum rule of differentiation problems step by step online.

$\frac{d}{dx}\left(\ln\left(1+\sqrt{\sin\left(x\right)}\right)-\ln\left(1-\sqrt{\sin\left(x\right)}\right)+2\arctan\left(\sqrt{\sin\left(x\right)}\right)\right)$

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(ln((1+sin(x)^(1/2))/(1-sin(x)^(1/2)))+2arctan(sin(x)^(1/2))) using the sum rule. Simplify the derivative by applying the properties of logarithms. 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. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}.