\( (1,1) \) বিন্দুতে \( y = e^{\ln(x-1/x)} - x > 0 \); বক্ররেখার ঢাল কত?

Explanation: Solve: \(y = e^{\ln\left(x - \frac{1}{x}\right)} - x = x - \frac{1}{x} - x = -\frac{1}{x}\) \(\implies \frac{dy}{dx} = \frac{1}{x^2} \therefore (1, 1)\) বিন্দুতে ঢাল, \(\frac{dy}{dx} = \frac{1}{1^2} = 1\)+C4C12C2:C11C2:C7C2:C11C2:C14C12C2:C11C2:C15C12C2:C11C2:C16C2:C15C2:C16C12C2:C11C2:C24C2:C27C2:C31C12C2:C11C2:C33C12C2:C11C2:C36C12C2:C11C2:C37C12C2:C11C2:C38C12C2:C11C2:C40C2:C43C12C2:C11C2:C52

Another Explanation (5): ```html

দেওয়া আছে, \( y = e^{\ln(x-1/x)} - x \)

যেহেতু \( e^{\ln(x)} = x \), তাই আমরা লিখতে পারি,

\( y = x - \frac{1}{x} - x \)

\( y = -\frac{1}{x} \)

এখন, \( x \) এর সাপেক্ষে \( y \) এর অন্তরকলন করে ঢাল নির্ণয় করা যাক।

\( \frac{dy}{dx} = \frac{d}{dx} \left( -\frac{1}{x} \right) \)

\( \frac{dy}{dx} = \frac{1}{x^2} \)

\( (1,1) \) বিন্দুতে ঢাল হবে,

\( \left. \frac{dy}{dx} \right|_{(1,1)} = \frac{1}{1^2} = 1 \)

অতএব, \( (1,1) \) বিন্দুতে \( y = e^{\ln(x-1/x)} - x \) বক্ররেখার ঢাল \( 1 \)। 🎉

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