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प्रश्न
DIfferentiate x sin x w.r.t. tan x.
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उत्तर
Let u = x sin x and v = tan x.
Then we want to find `"du"/"dv"`
Differentiating u and v w.r.t. x, we get
`"du"/"dx" = "d"/"dx"(x sin x)`
= `x"d"/"dx"(sin x) + (sin x)."d"/"dx"(x)`
= x cos x + (sin x) x 1
= x cos x + sin x
and
`"dv"/"dx" = "d"/"dx"(tanx)` = sec2x
∴ `"du"/"dv" = (("du"/"dx"))/(("dv"/"dx")`
= `(x cos x + sin x)/(sec^2x)`.
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