finding derivative of f(x)=2 sqrt x+5/7+1/x^2+pi/2

[adevon2122]

Need help please to find the derivative of this function:

f(x)=2 sqrt x+5/7+1/x^2+pi/2

I haven't done any work yet, dont know where to start, thanks

 

[skeeter]

\(\displaystyle \L f(x) = 2\sqrt{x}+\frac{5}{7}+\frac{1}{x^2}+\frac{\pi}{2}\)

rewrite the function as ...

\(\displaystyle \L f(x) = 2x^{\frac{1}{2}}+\frac{5}{7}+x^{-2}+\frac{\pi}{2}\)

so you can use the power rule for derivatives. remember that the derivative of a constant is 0.

\(\displaystyle \L f'(x) = x^{-\frac{1}{2}} - 2x^{-3}\)

finish by cleaning up the algebra ...

\(\displaystyle \L f'(x) = \frac{1}{\sqrt{x}} - \frac{2}{x^3}\)