Exercise
$\frac{d}{dx}\left(-\frac{1}{\arctan\left(e^x\right)}\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Find the derivative d/dx(-1/arctan(e^x)). 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. The derivative of the constant function (-1) is equal to zero. x+0=x, where x is any expression.
Find the derivative d/dx(-1/arctan(e^x))
Final answer to the exercise
$\frac{e^x}{\left(1+e^{2x}\right)\arctan\left(e^x\right)^2}$