Final answer to the problem
Step-by-step Solution
Specify the solving method
The derivative of a sum of two or more functions is the sum of the derivatives of each function
Learn how to solve problems step by step online.
$\frac{d}{dx}\left(\frac{1}{\cos\left(x\right)}\right)+\frac{d}{dx}\left(\frac{-\cos\left(x\right)}{1+\sin\left(x\right)}\right)$
Learn how to solve problems step by step online. Find the derivative of 1/cos(x)+(-cos(x))/(1+sin(x)). The derivative of a sum of two or more functions is the sum of the derivatives of each function. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. Multiply -1 times -1.