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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability2 Marks
Question
Find the second-order derivatives of the function $x^{20}$
✓

Answer

Let us take $y = x^{20}$
Now,
$\frac{d y}{d x}=\frac{d}{d x}(x^{20})$
$= 20 x^{19}$​​​​​​​
Therefore,
$\frac{d^{2} y}{d x^{2}}=\frac{d}{d x}\left(20 x^{19}\right)=20 \frac{d}{d x}{\left(x^{19}\right)}$ = $20 \times 19 \times x^{18}$
$= 380 x^{18}$​​​​​​​

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