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`

Answer 1

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`