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Chapter 4: Q3MP (page 238)

Find ∂2y∂x∂θ.

Short Answer

Expert verified

The value of ∂2y∂x∂θ is 1.

Step by step solution

01

Given Information

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

02

Concept

To find out the value of ∂2y∂x∂θdifferentiate∂y∂θ=rcosθ.

03

Find the value of ∂2y∂x∂θ

Differentiate the given polar coordinates

∂y∂θ=rcosθ∂y∂θ=x∂2y∂x∂θ=∂∂x∂y∂θ∂2y∂x∂θ=∂∂xx∂2y∂x∂θ=1

Therefore the value of ∂2y∂x∂θ=1.

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