Question

help. first derivative of cos^4t-sin^4t. the answer is -2sin2t and no idea deriving the answer

Answer 1

Use the chain rule. Take the derivative of each term individually.

y=cos(t)^2-sin(t)^4

dy/dt=2(cos(t))*(-sin(t))-4*(sin(t)^3)*cos(t)

Factor out 2cos(t)

2cos(t)[-sin(t)-2sin(t)^3]

Now factor out sin(t)

2cos(t)sin(t)[-1-2sin(t)^2]

2cos(t)sin(t)=sin(2t); trig identity

sin(2t)[-1-2sin(t)^2]

Here's where the issue is. Are you sure you wrote the problem down correctly/the book is right? If it were a -1 or a positive 2sin(t)^2, we could easily simplify this. I have spent quite a while trying to find a mistake in my math above, but could not. The key is that it's a trig identity--I'm just not sure how. Do you have the name of your textbook and the section/problem number?

Answer 2

its differential calculus by love rain