First Principles of Derivatives MCQ Quiz in मल्याळम - Objective Question with Answer for First Principles of Derivatives - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക
Last updated on Apr 9, 2025
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First Principles of Derivatives Question 1:
If f(x) = x3sinx, Find f'(x)
Answer (Detailed Solution Below)
First Principles of Derivatives Question 1 Detailed Solution
Concept:
\(\rm \frac{\mathrm{d} (x^{n})}{\mathrm{d} x} = nx^{n-1} \)
\(\rm \frac{\mathrm{d} (uv)}{\mathrm{d} x} = u\frac{\mathrm{d} v}{\mathrm{d} x} + v \frac{\mathrm{d} u}{\mathrm{d} x}\)
\(\rm \frac{\mathrm{d} (\sin x)}{\mathrm{d} x} = \cos x\)
Calculation:
Given: f(x) = x3sinx
f'(x) = \(\rm \frac{\mathrm{d} (x^{3}sinx)}{\mathrm{d} x}\)
⇒ \(\rm \frac{\mathrm{d} (x^{3}sinx)}{\mathrm{d} x} = x^{3}\frac{\mathrm{d} (sinx)}{\mathrm{d} x} + sinx \frac{\mathrm{d} x^{3}}{\mathrm{d} x}\)
= x3 cos x + sin x 3x2
= x2(x cos x + 3sin x)
∴ The required value is x2(x cos x + 3sin x).