Chapter 4: Q3MP (page 238)

Find $\frac{\partial^{2} y}{\partial x \partial θ}$ .

Short Answer

Expert verified

The value of $\frac{\partial^{2} y}{\partial x \partial θ}$ is 1.

Step by step solution

Given Information

Given that $r^{2} = x^{2} + y^{2}$ and the polar coordinates are $x = r \cos θ, y = r \sin θ$ .

Concept

To find out the value of $\frac{\partial^{2} y}{\partial x \partial θ}$ differentiate $\frac{\partial y}{\partial θ} = r c o s θ$ .

Find the value of ∂2y∂x∂θ

Differentiate the given polar coordinates

$\frac{\partial y}{\partial θ} = r \cos θ \frac{\partial y}{\partial θ} = x \frac{\partial^{2} y}{\partial x \partial θ} = \frac{\partial}{\partial x} (\frac{\partial y}{\partial θ}) \frac{\partial^{2} y}{\partial x \partial θ} = \frac{\partial}{\partial x} (x) \frac{\partial^{2} y}{\partial x \partial θ} = 1$

Therefore the value of $\frac{\partial^{2} y}{\partial x \partial θ} = 1$ .

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Find $\frac{\partial^{2} y}{\partial x \partial θ}$ .

Short Answer

Step by step solution

Given Information

Concept

Find the value of ∂2y∂x∂θ

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Find ∂2y∂x∂θ.

Short Answer

Step by step solution

Given Information

Concept

Find the value of ∂2y∂x∂θ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Famous Physicists

Turning Points in Physics

Electricity

Linear Momentum

Magnetism

Waves Physics

Study anywhere. Anytime. Across all devices.

Find $\frac{\partial^{2} y}{\partial x \partial θ}$ .