Find dy/dx when y = Ln (sinh 2x). A. 2 cosh 2x B. 2 sech 2x C. 2 coth 2x D. 2 csch 2x

Question

asked Jan 2, 2019 178k views

1 Answer

Radim Burget · Answer 1 · 2019-01-09T20:14:56+0000

The function given is a composite function. Let's work from the outside in:

y=(ln(sinh(2x)))

First step:

(d)/(dx)[y]= (d)/(dx)[ln(sinh(2x))]

Now, let's work it out:

(dy)/(dx) = (1)/(sinh(2x) ) * (d)/(dx)[sinh(2x)]

Next step:

(dy)/(dx) = (1)/(sinh(2x) ) * cosh(2x) * (d)/(dx)[2x]

Next step:

(dy)/(dx) = (1)/(sinh(2x) ) * cosh(2x) *2

Simplify:

Simplify further:

(dy)/(dx) = 2 ((cosh(2x))/(sinh(2x)))

Remember that:

{(cosh(x))/(sinh(x)) = coth(x)

So, your final answer is:

$\boxed{ (dy)/(dx) = 2coth(2x) }$

So, your answer is C. Hope I could help you!