1. ## Partial derivatives

Find the first partial derivatives of f(x,y,z) = z * arctan (y/x) :at the point (1, 1, 5).

I need serious help . i

2. Originally Posted by simsima_1
Find the first partial derivatives of f(x,y,z) = z * arctan (y/x) :at the point (1, 1, 5).

I need serious help . i
So you for first partial in z, you take the derivative as if everything except for z is a variable.

since:

$f(x,y,z)=z* arctan(\frac{y}{x})$

then if z is the only varible, everything attached to it is just some number so you can view the arctan as a constant, say b.

so:

$f(x,y,z)=z*b$

and the partial derivative of that in terms of z then is:

$f_z(x,y,z)=b$

we substitute b back in and get:

$f_z(x,y,z)=arctan(\frac{y}{x})$

can you do the rest from there?

3. One more question.... How would i take the partial derivative of the arctangent while holding one of the variables constant?

4. you just take the derivative of arctangent like normal and the other "variables" you just consider them to be constants so like:

what's the derivative of:

arctangent (2x)

$\frac{d}{dx}(arctan (2x)=\frac{1}{1+(2x)^2}*\frac{d}{dx}(2x)=\frac{2}{ 1+4x^2}$

So you can treat the other variables like that 2, they're constants, just that you don't know their value.