derivative of tanh^2(8x) ??

Question

what is the derivative of tanh^2(8x) ?? please be as specific and detailistic as possible with your answer.

Answer 1

use the chain rule from the general:
d/dx(tanh) = 1 - tanh^2(x)

Or you can work out from fundamentals by substituting (e^x - e^-x)/(e^x + e^-x) and then applying chain rule and (u/v)' formula...

Answer 2

If you are learning about tanh, then you can do this.

chain rule applies--twice. derivative of the outside (think of tanh as u^2) times with inside left alone (tanh) x derivative of the inside (tanh(8x)). Use a chain rule on the last step since this is tanh(8x) as well.

hint, d(tanh) = sech^2

Answer 3

Use the chain rule.

d[(tanh²8x)]/dx

= 2(tanh 8x)(sech²8x)(8)

= 16(tanh 8x)(sech²8x)
____________

This relies on knowing the derivative of tanh x. It is sech²x. If you don't know that use the quotient rule and work out the deriviative of

tahn x = sinh x / cosh x

Answer 4

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Answer 5

2*8*8tanh(8x) * sech^2(8x)
=128 tanh(8x)sech^2(8x)