Differentiability problem .

Question

Hi can someone help me with the following problem. I am having difficulties evaluating :

$$ \frac {d} {dt} f'(u(t)) $$

Is it just $f''(u(t))$ ?

Thanks

Answer 1

here $\frac{d}{dt}(f'(u(t)))=u'(t)f''(u(t))$, simply by applying the chain rule for composite functions:

if $h(t)=f(g(t))$, then $h'(t)=g'(t)f'(g(t))$.