Find the second order derivatives of the function.

Question:

Find the second order derivatives of the function.

$x^{20}$

Solution:

Let $y=x^{20}$

Then

$\frac{d y}{d x}=\frac{d}{d x}\left(x^{20}\right)=20 x^{19}$

$\therefore \frac{d^{2} y}{d x^{2}}=\frac{d}{d x}\left(20 x^{19}\right)=20 \frac{d}{d x}\left(x^{19}\right)=20 \cdot 19 \cdot x^{18}=380 x^{18}$

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