If y-x4-5ex-9- then d2ydx2 is

Given, nbsp;y=x^4+5e^x+9 So, d^2ydx^2=d(dydx)dx We have nbsp; dydx=d(x^4+5e^x+9)dx ⇒ dx^4dx+5de^xdx+d9dx ⇒ 4x^3+5e^x Now, nbsp;d^2ydx^2=d(4x^3+5e^x)dx ⇒ ...

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Byju's Answer

Standard XII

Physics

Basic Differentiation Rule

If y=x4+5ex+9...

Question

If $y = x^{4} + 5 e^{x} + 9$ , then $\frac{d^{2} y}{d x^{2}}$ is

4 x^{3} + 5 e^{x}

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\frac{x^{3}}{4} + \frac{e^{x}}{5}

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4 x^{3} + 5 e^{x} + 9

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12 x^{2} + 5 e^{x}

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Solution

The correct option is D $12 x^{2} + 5 e^{x}$
Given, $y = x^{4} + 5 e^{x} + 9$
So, $\frac{d^{2} y}{d x^{2}} = \frac{d (\frac{d y}{d x})}{d x}$
We have
$\frac{d y}{d x} = \frac{d (x^{4} + 5 e^{x} + 9)}{d x}$
$\Rightarrow \frac{d x^{4}}{d x} + 5 \frac{d e^{x}}{d x} + \frac{d 9}{d x}$
$\Rightarrow 4 x^{3} + 5 e^{x}$
Now, $\frac{d^{2} y}{d x^{2}} = \frac{d (4 x^{3} + 5 e^{x})}{d x}$
$\Rightarrow 4 \frac{d x^{3}}{d x} + 5 \frac{d e^{x}}{d x}$
$\Rightarrow 12 x^{2} + 5 e^{x}$

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If y=x4+5ex+9, then d2ydx2 is

The correct option is D 12x2+5exGiven, y=x4+5ex+9 So, d2ydx2=d(dydx)dx We have dydx=d(x4+5ex+9)dx ⇒ dx4dx+5dexdx+d9dx ⇒ 4x3+5ex Now, d2ydx2=d(4x3+5ex)dx ⇒ 4dx3dx+5dexdx ⇒ 12x2+5ex

If $y = x^{4} + 5 e^{x} + 9$ , then $\frac{d^{2} y}{d x^{2}}$ is