A) \[\cos \,\left( \frac{5x+1}{10{{x}^{2}}-3} \right)\,\frac{dy}{dx}\,\left( \frac{5x+1}{10{{x}^{2}}-3} \right)\]
B) \[\frac{5x+1}{10{{x}^{2}}-3}\,\,\cos \,\left( \frac{5x+1}{10{{x}^{2}}-3} \right)\]
C) \[\cos \,\left( \frac{5x+1}{10{{x}^{2}}-3} \right)\]
D) None of these
Correct Answer: A
Solution :
Suppose that \[t=\frac{5x+1}{10{{x}^{2}}-3},\] so \[y=f(t)\] \[\therefore \,\,\frac{dy}{dx}={f}'(t).\frac{dt}{dx}\] [Since \[f'(x)=\cos x\]] \[\frac{dy}{dx}=\cos \left( \frac{5x+1}{10{{x}^{2}}-3} \right)\,\frac{d}{dx}\,\left( \frac{5x+1}{10{{x}^{2}}-3} \right).\]
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