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Find d2ydx2, if y = x5 - Mathematics and Statistics

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Question

Find $\frac{d^{2} y}{{dx}^{2}}$ , if y = $x^{5}$

Sum

Solution

y = $x^{5}$

Differentiating both sides w.r.t.x, we get

$\frac{dy}{dx} = 5 x^{4}$

Again, differentiating both sides w.r.t. x , we get

$\frac{d^{2} y}{{dx}^{2}} = 5 \cdot \frac{d}{dx} (x^{4})$

$= 5 (4 x^{3})$

∴ $\frac{d^{2} y}{{dx}^{2}} = 20 x^{3}$

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Second Order Derivative

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Q 1. 2)Q 1. 1)Q 1. 3)

Chapter 3: Differentiation - EXERCISE 3.6 [Page 98]

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Balbharati Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board

Chapter 3 Differentiation
EXERCISE 3.6 | Q 1. 2) | Page 98

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