Understanding the Derivative of F(x, y, z) = tanh (x+2y+3z)

[makyol]

f(x, y, z) ?

Hey there,

Sorry for the title, but i cannot find any appropriate one for it, here is my question!

If f(x, y, z) = tanh (x+2y+3z) => fx =?(what is the derivative of f(x, y, z) with respect to x?)

Actually, i know the answer but i do not get the idea! In case it might help, the answer is that: sech^2(x+2y+3z)

So, as i said, can someone explain it to me? How can they reach this answer? Thanks!

 

[Mark44]

Hey there,

Sorry for the title, but i cannot find any appropriate one for it, here is my question!

If f(x, y, z) = tanh (x+2y+3z) => fx =?(what is the derivative of f(x, y, z) with respect to x?)

Actually, i know the answer but i do not get the idea! In case it might help, the answer is that: sech^2(x+2y+3z)

So, as i said, can someone explain it to me? How can they reach this answer? Thanks!

What you want is the partial derivative with respect to x. And you'll need the chain rule here, which looks something like this.
$$\frac{\partial tanh(u)}{\partial x} = \frac{\partial tanh(u)}{\partial u} \cdot \frac{\partial u}{\partial x}$$

 

[makyol]

Oh, i see now, i made a dummy mistake. Thank you for your quick reply!