Question

partial derivative with respect to X and y for (x^2 +y^2)cos(1/(√x^2+y^2) )​

Answer 1

Answer:

Let f(x,y)=y3x2f(x,y)=y3x2. Calculate ∂f∂x(x,y)∂f∂x(x,y).

Solution: To calculate ∂f∂x(x,y)∂f∂x(x,y), we simply view yy as being a fixed number and calculate the ordinary derivative with respect to xx. The first time you do this, it might be easiest to set y=by=b, where bb is a constant, to remind you that you should treat yy as though it were number rather than a variable. Then, the partial derivative ∂f∂x(x,y)∂f∂x(x,y) is the same as the ordinary derivative of the function g(x)=b3x2g(x)=b3x2. Using the rules for ordinary differentiation, we know that

dgdx(x)=2b3x.

dgdx(x)=2b3x.

Now, we remember that b=yb=y and substitute yy back in to conclude that

∂f∂x(x,y)=2y3x.