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If $y=x^2log_ex, $ then $\frac{d^2y}{dx^2}$ is equal to : |
$5+x\, log_e\, x$ $3+2\, log_e\, x$ $3+2x\, log_e\, x$ $x(1+2\, log_e, x)$ |
$3+2\, log_e\, x$ |
The correct answer is Option (2) → $3+2\log_e\, x$ $y=x^2\log_ex$ $\frac{dy}{dx}=2x\log_ex+x^2×\frac{1}{x}=2x\log_ex+x$ $⇒\frac{d^2y}{dx^2}=2\left(\log_ex+x^2×\frac{1}{x}\right)+1$ $=2(\log_ex+1)+1$ $=2\log_ex+3$ |
