Partial Derivatives of arcsin(xy) at (1, 0, pi/2), etc.

[Guest]

I need MAJOR help with partial derivatives!

f(x,y) = arcsin(xy) at (1,0,pi/2)
I know the derivative of arcsin = (1-x^2)^-.5

How does that work with partial derivatives though? And how do I plug the point in?

Also how would I take the first partial derivatives of tanh(3x-2y)?

 

[pka]

\(\displaystyle \L
f = \arcsin (xy)\quad \Rightarrow \quad f_x = \frac{y}{{\sqrt {1 - (xy)^2 } }}\quad \& \quad f_y = \frac{x}{{\sqrt {1 - (xy)^2 } }}\)

 

[galactus]

Remember the chain rule.

What's the derivative of \(\displaystyle tanh(x)\)?. That's right \(\displaystyle sech^{2}(x)\)

\(\displaystyle \L\\tanh(3x-2y)dx=3sech^{2}(3x-2y)\)

\(\displaystyle \L\\tanh(3x-2y)dy=-2sech^{2}(3x-2y)\)