Derivative

123

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Calculate the function f(x)=2x+1x\displaystyle f(x)=\sqrt{2x}+\frac{1}{x} the derivative at a point x=2\displaystyle x=2
 
123 said:
Calculate the function f(x)=2x+1x\displaystyle f(x)=\sqrt{2x}+\frac{1}{x} the derivative at a point x=2\displaystyle x=2

Exactly where are you stuck?

find derivative of ?(2x)

find derivative of 1/x

add those up

evaluate at x = 2

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.
 
so first i need find derivative of function and then add 2?
 
f(x)=1x+1x=\displaystyle f'(x)=\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{x}}=\(\displaystyle {\frac{2}{\sqrt{x}}\)???
 
123 said:
f(x)=1x+1x=\displaystyle f'(x)=\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{x}}=\(\displaystyle {\frac{2}{\sqrt{x}}\)???

Incorrect

d(2x)dx = 2121x\displaystyle \frac{d(\sqrt{2x})}{dx} \ = \ \sqrt{2} \cdot \frac{1}{2} \frac{1}{\sqrt{x}}

now find derivative of (1/x)
 
(1x)=1x2\displaystyle {(\frac{1}{x})}'=-\frac{1}{x^2}?
 

so

f(x) = 2x + 1x\displaystyle f(x) \ = \ \sqrt{2x} \ + \ \frac{1}{x}

dfdx = d(2x)dx + d(1x)dx\displaystyle \frac{df}{dx} \ = \ \frac{d( \sqrt{2x})}{dx} \ + \ \frac{d\left ( \frac{1}{x}\right )}{dx}

Now add those up to find f'(x) - then evaluate f'(2).
 
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