WEBVTT
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Hey, it's Claire. So ending. Read here
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. So for part A, we're going to use
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the first turret, the product roll, to find
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the first trip it is. And then we're going
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to use the product roll on both products to find
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the second derivative turns the derivative of G plus f
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of x times, a second or a bit of
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G of X, just equal to the second derivative
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of friends G of X plus two terms. The
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first derivative of terms derivative of G plus that F
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G comes the second derivative of G for part B
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, we have the equation for the second derivative.
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We're gonna difference you again to get the third derivative
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we got. Dream the second derivative drag this.
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And when we simplify it, we get three times
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the first derivative of the second derivative of G plus
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the terms such a threat of dirt derivative of G
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. We're gonna different. She again me yet I
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have to. The fourth is equal to this becomes
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equal Thio to the fourth three plus six back to
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the second derivative G to the second derivative plus four
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tongues, the derivative of G character of it.
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If and then for part C, we see that
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where we're going to recall the 2nd 3rd and fourth
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derivatives. And we see the coefficient. So for
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the half, or the coefficient of each derivative for
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the seconds we have 1 to 1. For the
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third, we have 1331 And for the fourth,
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we have one for six for one. So these
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are the paschal triangles. And you think if I
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know meal expression, this is our formula to the
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n minus K terms G to the key.