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Solve the following problem. Obtain derivative of the following function: xsin x - Physics

Sum

Solve the following problem.

Obtain derivative of the following function: `"x"/"sin x"`

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Solution

Using `"d"/"dx" [("f"_1("x"))/("f"_2("x"))] = 1/("f"_2("x")) ("df"_1("x"))/"dx" - ("f"_1("x"))/("f"_2^2("x")) ("df"_2("x"))/"dx"`

For f1(x) = x and f2(x) = sin x

∴ `"d"/"dx"("x"/"sin x") = 1/"sin x" xx ("d"("x"))/"dx" - "x"/sin^2"x" xx ("d"(sin "x"))/"dx"`

`= 1/"sin x" xx 1 - "x"/("sin"^2"x") xx cos "x"   .....[because "d"/"dx" ("sin x") = "cos x"]`

`= 1/"sin x" - "x cos x"/sin^2"x"`

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APPEARS IN

Balbharati Physics 11th Standard Maharashtra State Board
Chapter 2 Mathematical Methods
Exercises | Q 3. (v)(iii) | Page 29
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