# Derivative of arctan in a partial derivative

• Sep 11th 2010, 08:07 AM
tinyone
Derivative of arctan in a partial derivative
Im working on the derivative f'y(x,y) of the function f(x,y)=arctan(x^2)+ y^3

Because it's a derivative with respect to the variable y, this means that the variable x is held constant, does this mean that the entire arctan(x^2) should be regarded as just a number so the partial derivative equals to 3y^2 in the end??
• Sep 11th 2010, 08:28 AM
Plato
Quote:

Originally Posted by tinyone
Im working on the derivative f'y(x,y) of the function f(x,y)=arctan(x^2)+ y^3
Because it's a derivative with respect to the variable y, this means that the variable x is held constant, does this mean that the entire arctan(x^2) should be regarded as just a number so the partial derivative equals to 3y^2 in the end??

You are correct.
• Sep 12th 2010, 06:41 AM
tinyone
Cheers,

Derivative f'z(x,y,z) = 2(z+3)^4 + ln(xyz)

So keeping y and x constant would give me: f'z= 8(z+3)^3 + (1/xyz) * xy
• Sep 12th 2010, 01:52 PM
HallsofIvy
Quote:

Originally Posted by tinyone
Cheers,

$f_z= 8(z+ 3)^3+ \frac{1}{z}$