Question

How is this ?
Explain

Answer 1

Explanation:

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Answer 2

Answer:

Here 3 basic formula of differenciation are applied.

1) The differenciation of a constant is always 0.

2) d/dx(a^n) = n a^n-1

3)d/dx (uv) = u×d/dx(v) + v×d/dx(u) [Product rule of differenciation]

Explanation:

Here PV^γ is a constant. The differenciation of a constant is always 0. Here d/dx (PV^γ) or ∆(PV^γ) is same and becomes 0 due to constant differenciation.

Moreover another formula is applied here. d/dx(a^n) = n a^n-1

Applying product rule for differenciation given as d/dx (uv) = u×d/dx(v) + v×d/dx(u) and using the above formula,

we get PγV^γ-1∆V + V^γ∆P = 0.

NOTE : Here d/dx (PV^γ) is more appropriate and correct as compared to ∆(PV^γ).