Method of DifferentiationeasyFree

Method of Differentiation: Question

JEE Maths question with a full step-by-step solution.

Question
If f(x)=∣cos⁡x∣f(x) = |\cos x|, then f′(3π4)f'\left(\frac{3\pi}{4}\right) is:
A2\sqrt{2}
B−12-\frac{1}{\sqrt{2}}
C12\frac{1}{\sqrt{2}}correct
D−2-\sqrt{2}
Solution
Remove the modulus near x=3π4x = \frac{3\pi}{4} At x=3π4x = \frac{3\pi}{4}, cos⁡x<0\cos x < 0, so ∣cos⁡x∣=−cos⁡x|\cos x| = -\cos x. Hence f(x)=−cos⁡xf(x) = -\cos x. Step 2: Differentiate and evaluate
f′(x)=sin⁡x  ⟹  f′(3π4)=sin⁡3π4=12f'(x) = \sin x \implies f'\left(\frac{3\pi}{4}\right) = \sin\frac{3\pi}{4} = \frac{1}{\sqrt{2}}
 Answer: (3)
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