Exercise
$\frac{d}{dx}x\sqrt{1-x^2}+cos^{-1}x$
Step-by-step Solution
Learn how to solve problems step by step online. Find the derivative d/dx(x(1-x^2)^(1/2)+arccos(x)) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\sqrt{1-x^2}. 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}.
Find the derivative d/dx(x(1-x^2)^(1/2)+arccos(x)) using the sum rule
Final answer to the exercise
$\sqrt{1-x^2}+\frac{-x^2-1}{\sqrt{1-x^2}}$