anonymous
  • anonymous
From Unit 1 Differentiation exercise 1G-5b... The problem gives Leibniz' formula for the nth derivative of a product of two functions and then asks to apply the formula to y=x^p(1+x)^q in order to find the y^(p+q) derivative of the function. I've tried to solve using (p+q) as the n of the summation of the formula, should I consider to be moving both values or just p or q? Could someone please help me understand better this problem? Thank you in advance
OCW Scholar - Single Variable Calculus
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
The problem gives you the following function\[y=x^p(1+x)^{q}\]and asks you to use Leibniz' formula (which is given as part of the problem) to produce a formula for the (p+q)th derivative of that function. To give a concrete example, if p=7 and q=12 you would have to find the 19th derivative of\[y=x^7(1+x)^{12}\]When you apply Leibniz' formula you'll see that some terms drop out. In my example, the first term would be\[(x^7)^{(19)}(1+x)^{12}\]In other words, the 19th derivative of x^7, multiplied by (1+x)^12. The 19th derivative of x^7 is obviously zero, so this term drops out. You have to figure out what's left after dropping out the terms that evaluate to zero.
anonymous
  • anonymous
thank you, you were very clear

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