Differentiate 2x/ x with respect to x.

Correct Answer is : 2csc⁡x(1−xcot⁡x)2 x(1 - x x)2cscx(1−xcotx)

Correct Answer is : 2csc⁡x(1−xcot⁡x)2 x(1 - x x)2cscx(1−xcotx)

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JAMB Mathematics 2019 Paper

Question : 72

Total: 73

Differentiate

\frac{2x}{\sin x}

with respect to x.

Solution:

Concept:

Differentiate

\frac{2x}{\sin x}

using the quotient rule or rewrite as

2x \csc x

Explanation:

Let

y = \frac{2x}{\sin x}

Using the quotient rule,

\frac{dy}{dx} = \frac{(\sin x)(2) - 2x(\cos x)}{\sin^2 x}

Simplify:

\frac{2\sin x - 2x\cos x}{\sin^2 x}

Rewrite as

2\csc x - 2x\cot x\csc x

Factor:

2\csc x(1 - x\cot x)

Answer:

2\csc x(1 - x\cot x)

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