Exercise
$\frac{d}{dx}\left(x\sqrt{x^2-1}\right)$
Step-by-step Solution
Learn how to solve sum rule of differentiation problems step by step online. Find the derivative of x(x^2-1)^(1/2). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\sqrt{x^2-1}. The derivative of the linear function is equal to 1. 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 x(x^2-1)^(1/2)
Final answer to the exercise
$\sqrt{x^2-1}+\frac{x^2}{\sqrt{x^2-1}}$