- #1

songoku

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- Homework Statement
- Please see below

- Relevant Equations
- Partial derivative

Integration (maybe)

My attempt:

$$\frac{\partial f}{\partial x}=-\sin y + \frac{1}{1-xy}$$

$$\int \partial f=\int (-\sin y+\frac{1}{1-xy})\partial x$$

$$f=-x~\sin y-\frac{1}{y} \ln |1-xy|+c$$

Using ##f(0, y)=2 \sin y + y^3##:

$$c=2 \sin y + y^3$$

So:

$$f(x,y)=-x~\sin y-\frac{1}{y} \ln |1-xy|+2 \sin y + y^3$$

Is my answer correct? In the lesson itself, there is no integration when learning partial derivative but I can't think of any other way to solve the question without integration.

Thanks