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Question
Fill in the blanks:
y = (3x2 + 5) cos x
Differentiating w.r.t.x
`("d"y)/("d"x) = "d"/("d"x) [(3x^2 + 5) cos x]`
= `(3x^2 + 5) "d"/("d"x) [square] + cos x "d"/("d"x) [square]`
= `(3x^2 + 5) [square] + cos x [square]`
∴ `(dx)/("d"y) = (3x^2 + 5) [square] + [square] cos x`
Solution
y = (3x2 + 5) cos x
Differentiating w.r.t.x,
`("d"y)/("d"x) = "d"/("d"x) [(3x^2 + 5) cos x]`
= `(3x^2 + 5) "d"/("d"x) [cos x] + cos x "d"/("d"x) [3x^2 + 5]`
= `(3x^2 + 5) [- sin x] + cos x [6x + 0]`
∴ `(dx)/("d"y) = (3x^2 + 5) [- sin x] + [6x] cos x`
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