Maximizing Efficiency: Applying the Chain Rule in Differentiating AC Sources

[maali5]

Homework Statement

Chain/product or quotient

Homework Equations

v=4sin^3 (4t)

The Attempt at a Solution

NB:@ Means teta(spelling might be wrong)

4sin^3 (4t) = 4sin (4t).sin (4t).sin (4t)

using sin^2@=1-cos 2@ /2


v= 4sin (4t). (1-cos 2@ /2)


= 4sin (4t)/2 . 4sin (4t). cos (8t)/2

= 2 sin (4t) - 2 sin (4t) cos (8t)




then I done some calculation containing product and chain rule with a final answer of


dv/dt = 8 cos (4t) + 16 sin (4t) sin (8t) - 8 cos (4t) cos (8t)



Thanx for your help

 

[tiny-tim]

hi maali5!

v= 4sin (4t). (1-cos 2@ /2)

no, v= 4sin (4t). (1-cos 2@)/2

but anyway you should have used the chain rule, with g(t) = sin(4t) ​