Another Diff Problem

[Jason76]

\(\displaystyle f(x) = \sqrt{3} x + \sqrt{2x}\)

\(\displaystyle f(x) = (3)^{1/2} x + (2x)^{1/2}\)

\(\displaystyle f'(x) = ? + \dfrac{1}{2}(2x)^{-1/2}\)

\(\displaystyle f'(x) = ? + x^{-1/2}\)

 

[Deleted member 4993]

\(\displaystyle f(x) = \sqrt{3} x + \sqrt{2x}\)

\(\displaystyle f(x) = (3)^{1/2} x + (2x)^{1/2}\)

\(\displaystyle f'(x) = ? + \dfrac{1}{2}(2x)^{-1/2}\)

\(\displaystyle f'(x) = ? + x^{-1/2}\)

\(\displaystyle \frac {d}{dx}[C*x] \ = \ C \)

 

[Jason76]

Since, at this point, were not supposed to know the chain rule, then this was how it's supposed to come out:

\(\displaystyle f(x) = \sqrt{3} x + \sqrt{2x}\)

\(\displaystyle f(x) = \sqrt{3} * x + \sqrt{2} * \sqrt{x}\)

\(\displaystyle f(x) = \sqrt{3} * x + \sqrt{2} * x^{1/2}\)

\(\displaystyle f'(x) = \sqrt{3} * 1 + \sqrt{2} * \dfrac{1}{2}x^{-1/2}\) Answer