Question

how do you differentiate f(t)=46+2sin(2t/3)?

Answer 1

i think you need to use chain rule. the 2 in front of sine is throwing me off a bit i admit.

the derivative of 46 is 0. and then with chain rule. \[2\sin (2t/3)^1 \] do the outside function first, in this case sine. so using power rule, you bring the 1 infront of the 2. and then subtract 1 from the exponent. then the derivative of sin(x) is cos(x).

\[1*2\cos (2t/3)\]
then you multiply by the derivative of the inside (2t/3)

\[(2t/3)=2t*1/3\]
power makes the derivative equal 2 and so

\[2\cos (2t/3)*2=4\cos (2t/3)\]

Answer 2

thank you!

Answer 3

4/3 is in front