Question
Download Solution PDFमान लीजिए \(\rm f(x) = log x^3 + 2 x^2 -3x + 100\) है, तो f'(3) का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
यदि f(x) = xn है, तो f'(x) = \(\rm n x^{n-1}\) है।
f(x) = logx है, तो f'(x) = \(\rm 1\over x\) है।
f(x) = स्थिरांक है, तो f'(x) = 0 है।
log mn = n log m
गणना:
\(\rm f(x) = log x^3 + 2 x^2 -3x\)
⇒ \(\rm f(x) = 3log x + 2 x^2 -3x\)
⇒ \(\rm f'(x) = 3{\frac {d} {dx}}log x + {\frac {d} {dx}}2 x^2 -{\frac {d} {dx}}3x\)
⇒ \(\rm f'(x) = {\frac {3} {x}}+ 4x -3\)
⇒ \(\rm f'(3) = {\frac {3} {3}}+ 4(3) -3\)
⇒ \(\rm f'(3) = 10\)
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