Differentiating tanh [Solved!]

X

what the answer if we differentiate `y = tanh (x-9)`?

Relevant page

<a href="/differentiation-transcendental/differentiate-transcendental-intro.php">Differentiation of Transcendental Functions</a>

What I've done so far

I tried to find this on IntMath, but couldn't.

X

Hello Haida

This is not "`tan`", but `"tanh`".

IntMath doesn't include the hyperbolic functions (yet), but you can see the formula for differentiating `tanh x` at:

<a href="/differentiation-transcendental/table-derivatives.php">Table of Derivatives</a>

Your situation is a function of function situation. Do you think you can do it now?
Good luck with it.

Regards

M Bourne

X

I think it's

Put `u=x-9` so `y= tanh u`.

Then `dy/dx = dy/(du) (du)/dx`

` = (1-tanh^2 u)(du)/dx = 1 - tanh^2(x-9)`.

Is it OK?

X

Yes, you've nailed it.

Well done.