Question
Download Solution PDFx के संबंध में sin(x) का दूसरा अवकलज क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFधारणा:
- \(\frac{d}{{dx}}\left( {{x^n}} \right) = n{x^{n - 1}}\)
जहां, 'x' एक बीजगणितीय फलन है
- \(\frac{d}{{dx}}\left( {\sin x} \right) = \cos x\)
- \(\frac{d}{{dx}}\left( {\cos x} \right) = - \sin x\)
- दूसरे अवकलज का निम्न रूप में प्रतिनिधित्व किया गया है
- \(\frac{{{d^2}y}}{{d{x^2}}} = \frac{d}{{dx}}\left( {\frac{{dy}}{{dx}}} \right)\)
अनुप्रयोग:
माना कि y = sinx
∴ \(\frac{{dy}}{{dx}} = \frac{d}{{dx}}\left( {\sin x} \right) = \cos x\)
अब x के संबंध में sin(x) का दूसरा अवकलज है
\(\frac{{{d^2}y}}{{d{x^2}}} = \frac{d}{{dx}}\left( {\cos x} \right)\)
\(\frac{{{d^2}y}}{{d{x^2}}} = - \sin x\)
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