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Question
Fill in the blanks:
y = `sinx/(x^2 + 2)`
Differentiating. w.r.t.x.
`("d"y)/("d"x) = (square "d"/("d"x) (sin x) - sin x "d"/("dx) square)/(x^2 + 2)^2`
= `(square square - sin x square)/(x^2 + 2)^2`
= `(square - square)/(x^2 + 2)^2`
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Solution
y = `sinx/(x^2 + 2)`
Differentiating. w.r.t.x., we get
`("d"y)/("d"x) = (x^2+ 2 "d"/("d"x) (sin x) - sin x "d"/("dx) x^2 + 2)/(x^2 + 2)^2`
= `((x^2 + 2) (cos x) - sin x (2x))/(x^2 + 2)^2`
= `((x^2 cos x + 2 cos x) - 2x sin x)/(x^2 + 2)^2`
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