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Chapter 12: Q. 37 (page 961)

Find the gradient of the given functions in Exercises 37鈥�42.

z=x2siny+ysinx

Short Answer

Expert verified

The gradient of the given function is2xsiny+ycosx,x2cosy+sinx.

Step by step solution

01

Step 1. Given Information.

The given function is:

z=x2siny+ysinx

02

Step 2. Calculation.

The gradient of the given function is:

z=fx,y=x2siny+ysinx鈭�f(x,y)=fxx,y,fyx,y-------(1)

Now find

fxx,y=2xsiny+ycosxfyx,y=x2cosy+sinx

Use these above values in (1) we get,

localid="1650186054791" 鈭�fx,y=2xsiny+ycosx,x2cosy+sinx

03

Step 3. Conclusion.

The gradient of the given function is 2xsiny+ycosx,x2cosy+sinx.

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