Question

F(t)=cos at. then find F'''(t)

Answer 1

Hello users....

We have given that
F(t) = cos at

We have to find
F'''(t) = ?

Solution:-
We know that
F'(cos ax) = -sin ax × f'(ax) = -a sin ax
And
F'(sin ax) = cos ax × f'(ax) = a cos ax

Now
F'(t) = F'( cos at)
= -a sin at
And
F''(t) = F'(-a sin at )
= -a F'(sin at ) = -a × ( a cos at)
= -a² cos at

Now
At last
F'''(t) = F'(-a² cos at )
= -a² F'(cos at)= -a² × (- a sin at)
= a³ sin at answer

Hence
F'''(t) = a³ sin at

✡✡ hope it helps ✡✡