Home » If y = cos 3x, find (frac{delta y}{delta x})

If y = cos 3x, find (frac{delta y}{delta x})

If y = cos 3x, find (frac{delta y}{delta x})
  • A.
    (frac{1}{3} sin 3x)
  • B.
    (-frac{1}{3} sin 3x)
  • C.
    3 sin 3x
  • D.
    -3 sin 3x
Correct Answer: Option D
Explanation

y = cos 3x
Let u = 3x so that y = cos u
Now, (frac{delta y}{delta x} = 3),
(frac{delta y}{delta x} = -sin u)
By the chain rule,
(frac{delta y}{delta x} = frac{delta y}{delta u} times frac{delta u}{delta x})
(frac{delta y}{delta x} = (-sin u) (3))
(frac{delta y}{delta x} = -3 sin u)
(frac{delta y}{delta x} = -3 sin 3x)

There is an explanation video available below.

Explanation Video

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