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Calculus and Analytic Geometry I

by: Angelina Steuber

Calculus and Analytic Geometry I MATH 151

Marketplace > Radford University > Mathematics (M) > MATH 151 > Calculus and Analytic Geometry I
Angelina Steuber
GPA 3.79

William Case

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William Case
Class Notes
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This 4 page Class Notes was uploaded by Angelina Steuber on Monday October 19, 2015. The Class Notes belongs to MATH 151 at Radford University taught by William Case in Fall. Since its upload, it has received 18 views. For similar materials see /class/224680/math-151-radford-university in Mathematics (M) at Radford University.

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Date Created: 10/19/15
Math 151 Section 23 Product and Quotient Rule The Product Rule If fx FxS x then f39x F39xS x S39x Fx Quotient Rule Tx BxT x T xB x I h f f x BmJ en f x BOW Example 1 Given fx x2 4xx2 3x find f m f x 1x2 4x2 3x 1x2 Ecsz 4x dx dx f x 2x 4x2 3x 2x 3x2 4x f x 2x3 6x2 4x2 12x 2x3 8x2 3x2 12x f x 4x3 21x2 24x Example 2 Given fx 5x3 4x2 4x2x2 6x find f x f39x 15 4x2 4xX2x2 6x 12x2 6xX5x3 4x2 4x dx dx f x 15x2 8x 42x2 6x 4x 65x3 4x2 4x Example 3 Given f x 4x36 find f 39x d fOC d 4163 1W x dx f x 12xzex 4x36 or f x 4xzex3 x Example 4 Find the derivative of f x ex sin x f x ex sin x i sin xex f x ex sinxex cosx Example 5 2 x Given foo 3x3 4x 5 find f39x 3x3 4x 51 ex x2 3x2 4 5 foo dx dx 2 2 3x 4x 5 3x3 4x 52x x2 9x2 4 3x3 4x 52 fx 6x4 8x2 10x 9x4 4x2 3x3 4x52 3x4 4x2 10x 3x3 4x52 f 39x fx Example 6 2 Given fx then f39x x 3x3 x2 3x 32x 5 x2 5x2x 3 f x x2 3x32 x 2 2x3 6x2 6x 5x2 15x15 2x3 10x2 3x2 15x x2 3x32 fx 2x3 11x2 21x15 2x3 13x2 15x x2 3x32 2x2 6x15 f X x2 3x32 Example 7 Given fx x26 2 then f39x A ik kt ik fr dx 2 2 dx 8 x 2 x2 2 X ex2x f X x2 22 xzex 26X 2xex f X x2 22 x2 2x 2 fm W Example 8 Find the derivative of gx g x x3 cos x 2cos xx3 x3 sin x cos x3x2 6 X 8 06 x2xsinx3cosx 6 X xsinx3cosx 4 X Example 9 Find the equation of a tangent line to the function f x x3ex at the point Le d X d X fxx3e ie x3 dx dx f39x 3x26 x3ex f 1 312e113e1 3e1e 46 y e4ex 1 y e4ex 4e y4ex 3e y 64x 3


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