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Chapter 4: Q4MP (page 238)

Find ∂2r∂θ∂y.

Short Answer

Expert verified

The value of ∂2r∂θ∂yiscosθ

Step by step solution

01

Given Information

Given that r2=x2+y2and the polar coordinates arex=rcosθ,y=rsinθ .

02

find the value of ∂2r∂θ∂y

The value of r is expressed as,

.r=x2+y2

The above equation differentiates with respect to y.

∂r∂y=yx2+y2∂r∂y=rsinθr2∂r∂y=sinθ\

Now,

∂2r∂θ∂y=∂∂θ∂r∂y∂2r∂θ∂y=∂∂θsinθ∂2r∂θ∂y=cosθ

Hence the value of ∂2r∂θ∂y=cosθ.

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