Question

what is the derivative of cosh^(3)t

Answer 1

-3sinxcosx^2.... i think but i just learned the chain rule

Answer 2

nope that's not it. I just checked :/ thank you for trying though!

Answer 3

-3sinxcosx(^2)x

Answer 4

its a hyperbolic function

Answer 5

how about 3(cosht)^2(sinh)?

Answer 6

3(cosh t)^2(sinh t) i meant

Answer 7

I like that one too Igbasallote

Answer 8

the diriveitive is cos is -sin... right?

Answer 9

Not for hyperbolic cos functions. Just for regular cos functions. These have a little trick to them.

Answer 10

[cosh^(3)t]' = [(cosh t)^3]' = 3*(cosh t)^2*[cosh t]' = 3*cosh^2(t)*sinh t

Answer 11

1/12(9sinh(x)+sinh3(x)) + C
because
formula says integral of cosh^m(x) = (sinh(x)cosh^(m-1) of (x))/m + ((m-1)/m)*integral of cosh^[m-2] of (x)

which becomes:

= 1/3 sinh(x) cosh^2(x)+2/3 integral cosh(x) dx
The integral of cosh(x) is sinh(x):
= (2 sinh(x))/3+1/3 sinh(x) cosh^2(x)+C
Which is equal to:
= 1/12 (9 sinh(x)+sinh(3 x))+C