Exercise
$\frac{d}{dx}\left(\left(x-4\sqrt{x}\right)+x\left(1-\frac{2}{\sqrt{x}}\right)\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Find the derivative d/dx(x-4x^(1/2)x(1+-2/(x^(1/2)))) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. 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=x and g=1+\frac{-2}{\sqrt{x}}. The derivative of the linear function is equal to 1.
Find the derivative d/dx(x-4x^(1/2)x(1+-2/(x^(1/2)))) using the sum rule
Final answer to the exercise
$2+\frac{-3}{\sqrt{x}}$