Exercise
$\frac{d}{dx}\frac{1-x^5}{1+x^5}$
Step-by-step Solution
Learn how to solve problems step by step online. Find the derivative d/dx((1-x^5)/(1+x^5)). 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}}. Simplify the product -(1-x^5). The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a sum of two or more functions is the sum of the derivatives of each function.
Find the derivative d/dx((1-x^5)/(1+x^5))
Final answer to the exercise
$\frac{5\left(-1-x^5\right)x^{4}+5\left(-1+x^5\right)x^{4}}{\left(1+x^5\right)^2}$