Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question
If f is a differentiable function, find an expression for the derivative of each of the following functions. (a) y = x²f(x) Ⓒy' = x6f '(x) - 6x7f(x) O y'=x7f '(x) + 7x6f(x) O y'= x7f(x) + 7x6f '(x) O y' = x²f(x) – 7x6f '(x) - O y'= xof '(x) + 6x f(x) (b) y = O y'= Oy' = f(x) x5 O y' = xf '(x) - 4f(x) 6 O y'=xf'(x) - 5f(x) +6 xf(x) + 5f '(x) x5 O y'= xf '(x) + 4f(x) x5 y = xf(x) = 5f '(x) +4 X ♥ (c) to f(x) O y'=f'(x)(6x5) — x6f(x) [f(x)]² O y' = f'(x)(5x5) - x6f '(x) [f(x)]² O y'= f(x)(5x6) + x6ƒ '(x) [f(x)]² HA چار
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Transcribed Image Text:If f is a differentiable function, find an expression for the derivative of each of the following functions. (a) y = x²f(x) Ⓒy' = x6f '(x) - 6x7f(x) O y'=x7f '(x) + 7x6f(x) O y'= x7f(x) + 7x6f '(x) O y' = x²f(x) – 7x6f '(x) - O y'= xof '(x) + 6x f(x) (b) y = O y'= Oy' = f(x) x5 O y' = xf '(x) - 4f(x) 6 O y'=xf'(x) - 5f(x) +6 xf(x) + 5f '(x) x5 O y'= xf '(x) + 4f(x) x5 y = xf(x) = 5f '(x) +4 X ♥ (c) to f(x) O y'=f'(x)(6x5) — x6f(x) [f(x)]² O y' = f'(x)(5x5) - x6f '(x) [f(x)]² O y'= f(x)(5x6) + x6ƒ '(x) [f(x)]² HA چار
+6 f(x) O y' = ƒ '(x)(6x5) – x6f(x) [f(x)]² (c) y = O y' = f '(x)(5x5) — xºƒ '(x) [f(x)]² O ○ y' = f(x)(5x6) + x6ƒ '(x) [f(x)]² O y' = f '(x)(5x6) + x5f(x) [f(x)]² O y' = f(x)(6x5) – x6f '(x) [f(x)]² (d) 3 + xf(x) VX O y'=xf(x) + 2x²f '(x), – 3 2x3/2 y = O y'= xf(x) + 3x²f(x) — 2′ 2x3/2 O y' = xf '(x) – 2x²f '(x) + 3 2x3/2 O y'= xf(x) — 3x²ƒ '(x) + 3 2x³/2 O y' = xf '(x) + 3x²f(x) − 2 2x3/2 MEN
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Transcribed Image Text:+6 f(x) O y' = ƒ '(x)(6x5) – x6f(x) [f(x)]² (c) y = O y' = f '(x)(5x5) — xºƒ '(x) [f(x)]² O ○ y' = f(x)(5x6) + x6ƒ '(x) [f(x)]² O y' = f '(x)(5x6) + x5f(x) [f(x)]² O y' = f(x)(6x5) – x6f '(x) [f(x)]² (d) 3 + xf(x) VX O y'=xf(x) + 2x²f '(x), – 3 2x3/2 y = O y'= xf(x) + 3x²f(x) — 2′ 2x3/2 O y' = xf '(x) – 2x²f '(x) + 3 2x3/2 O y'= xf(x) — 3x²ƒ '(x) + 3 2x³/2 O y' = xf '(x) + 3x²f(x) − 2 2x3/2 MEN
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