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.∂f∂x(x,y)=2y3x.
Example 2
For the same ff, calculate ∂f∂y(x,y)∂f∂y(x,y).
Solution: This time, we'll just calculate the derivative with respect to yy directly without replacing xx with a constant. We just have to remember to treat xx like a constant and use the rules for ordinary differentiation. We don't touch the x2x2 and only differentiate the y3y3 factor to calculate that
∂f∂y(x,y)=3x2y2.
try to use these two methods i also have same issue but my issue is resolve this this code
Source: Matlab experts Series
