Advertisements
Advertisements
प्रश्न
Solve the following problem.
Obtain derivative of the following function: `"x"/"sin x"`
उत्तर
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"`
APPEARS IN
संबंधित प्रश्न
Solve the following problem.
Obtain a derivative of the following function: x sin x
Solve the following problem.
Obtain derivative of the following function: x4 + cos x
Solve the following problem.
Using the rule for differentiation for quotient of two functions, prove that `"d"/"dx" ("sin x"/"cos x") = sec^2"x"`.
Solve the following problem.
Evaluate the following integral: \[\int_0^{\frac{\pi}{2}}\] sin x dx
Solve the following problem.
Evaluate the following integral: \[\int_1^5\] x dx
