Word Count : 354

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हम दिए गए फ़ंक्शन के पहले और दूसरे क्रम (first and second order) के आंशिक अवकलन (partial derivatives) को खोजेंगे। ### दिया गया फ़ंक्शन: \[ f(x, y) = \sin(xy) \] ### पहले क्रम के आंशिक अवकलन (First-Order Partial Derivatives) #### 1. \( f_x \) निकालना (Partial derivative w.r.t. \( x \)): \[ f_x = \frac{\partial}{\partial x} \sin(xy) \] चूँकि \( xy \) एक संयुक्त फलन (composite function) है, इसलिए चेन रूल (chain rule) लागू होगा: \[ f_x = \cos(xy) \cdot \frac{\partial}{\partial x} (xy) \] \[ f_x = \cos(xy) ________ ___ ________ _________ ______ ___.
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