Question

differentiation of r = ae^theta cot alpha​

Answer 1

Answer:

(α = alpha )

r= ae^θcotα

dr/dθ = a e^θcotα × cotα

dr/dθ = r cotα [ since ae^θcotα = r ]

Answer 2

Answer:

This represents the derivative of the polar coordinates r with respect to theta, with theta cot(alpha) as the function of x.

dr/dtheta = ae^(theta cot(alpha)) * (cot(alpha))

Step-by-step explanation:

To differentiate r = ae^(theta cot(alpha)), we can use the chain rule.

The chain rule states that if we have a function of the form y = f(u(x)), then the derivative of y with respect to x is given by:

dy/dx = dy/du * du/dx

In this case, we have:

r = ae^(theta cot(alpha))

So, we can let u(x) = theta cot(alpha) and f(u) = ae^u

Therefore,

dr/dtheta = ae^(theta cot(alpha)) * (cot(alpha))

This represents the derivative of the polar coordinates r with respect to theta, with theta cot(alpha) as the function of x.

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