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JAMB Mathematics 2014 Paper

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Question : 30

Total: 47

If y = cos 3x, find

\frac{\delta y}{\delta x}

$\frac{1}{3} \sin 3x$
$-\frac{1}{3} \sin 3x$
3 sin 3x
-3 sin 3x

Solution:

Concept:

Differentiate the composite function

y = \cos(3x)

using the chain rule.

Explanation:

Let

u = 3x

, so

y = \cos u

.

Differentiate

u

with respect to

x

:

\frac{du}{dx} = 3

.

Differentiate

y

with respect to

u

:

\frac{dy}{du} = -\sin u

.

Apply the chain rule:

\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}

.

Substitute the derivatives:

\frac{dy}{dx} = (-\sin u)(3)

.

Simplify:

\frac{dy}{dx} = -3\sin u

.

Replace

u

with

3x

:

\frac{dy}{dx} = -3\sin(3x)

.

Answer:

\frac{dy}{dx} = -3 \sin 3x

, so the correct option is D.

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