Solving: $\frac{d}{dx}\left(2\sqrt{x-1}\mathrm{arccsc}\left(\sqrt{x}\right)\right)$
Exercise
$\frac{dy}{dx}\left(2\sqrt{x-1}\arccsc\left(\sqrt{x}\right)\right)$
Step-by-step Solution
Learn how to solve differential calculus problems step by step online. Find the derivative of 2(x-1)^(1/2)arccsc(x^(1/2)). The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sqrt{x-1} and g=\mathrm{arccsc}\left(\sqrt{x}\right). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of a sum of two or more functions is the sum of the derivatives of each function.
Find the derivative of 2(x-1)^(1/2)arccsc(x^(1/2))
Final answer to the exercise
$\frac{\mathrm{arccsc}\left(\sqrt{x}\right)}{\sqrt{x-1}}+\frac{-1}{x}$