Given the function $f(h) = \rho gh - \sigma \big\{ \frac{h^{''}}{(1+(h^{'})^2)^{\frac{3}{2}}} \big\}$
assuming I am incrementing $h$ by $\phi$. that is
$f(h + \phi) = \rho g(h + \phi) - \sigma \big\{ \frac{(h + \phi)^{''}}{(1+((h + \phi)^{'})^2)^{\frac{3}{2}}} \big\}$.
Please I need help in understanding the step by step Taylor expansion of the above equation to arrive at the following result:
$f(h + \phi) = f(h) + \rho g\phi - \sigma \big\{ \frac{\frac{-3}{2}h^{'}h^{''}\phi ^{'}}{(1+(h^{'})^2)^{\frac{5}{2}}} + \frac{\phi ^{''}}{(1+(h^{'})^2)^{\frac{3}{2}}} \big \}$
Thanks in advance