If $y=e^{2x}$, then $\dfrac{d^2y}{dx^2}$ at $x=0$ is : (a) $2$ (b) $4$ (c) $0$ (d) $9$

If y=e2x, then (d²y)/(dx²) at x=0 is : (a) 2 (b) 4 (c) 0 (d) 9

Question 37 of 49

y=e^{2x}

(a)

2

(b)

4

(c)

0

(d)

9

Puducherry TnboardTamil Nadu HSC First Year (DGE) Commerce Board 2024MCQ· 1mImportance★★★★★

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For $y=e^{2x}$ , the second derivative at $x=0$ is $4$ .

Differentiate using the chain rule (the derivative of $e^{u}$ is $e^{u}\cdot u'$ ):

$\frac{dy}{dx}=e^{2x}\cdot 2 = 2e^{2x}.$

Differentiate again: …