Differentiate Sin (Cos(\( { x}^{ 2} \)))

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Continuity and Differentiability

Question:

Differentiate Sin (Cos(\( { x}^{ 2} \))) w.r.t. x

Options:

2x sin \( {x }^{2 } \) cos (cos \( { x}^{ 2} \))

-2x sin \( {x }^{2 } \) cos (cos \( { x}^{ 2} \))

2x sin \( {x }^{2 } \) sin (cos \( { x}^{ 2} \))

Correct Answer:

-2x sin \( {x }^{2 } \) cos (cos \( { x}^{ 2} \))

Explanation:

Use Chain Rule :

Sin (Cos(\( { x}^{ 2} \))) = -2x sin \( {x }^{2 } \) cos (cos \( { x}^{ 2} \))