Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Choose an option
- Find the derivative using the definition
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative using logarithmic differentiation
- Find the derivative
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Load more...
Taking the derivative of arccosecant
Learn how to solve problems step by step online.
$\frac{-1}{\frac{x+1}{x-1}\sqrt{\left(\frac{x+1}{x-1}\right)^2-1}}\frac{d}{dx}\left(\frac{x+1}{x-1}\right)$
Learn how to solve problems step by step online. Find the derivative of arccsc((x+1)/(x-1)). Taking the derivative of arccosecant. Divide fractions \frac{-1}{\frac{x+1}{x-1}\sqrt{\left(\frac{x+1}{x-1}\right)^2-1}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. 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}}. Multiplying fractions \frac{-\left(x-1\right)}{\left(x+1\right)\sqrt{\left(\frac{x+1}{x-1}\right)^2-1}} \times \frac{\frac{d}{dx}\left(x+1\right)\left(x-1\right)-\left(x+1\right)\frac{d}{dx}\left(x-1\right)}{\left(x-1\right)^2}.
