Differentiate these using the product rule. Write your answers in fully factorised form with the common factor before the brackets. y = x° (x² + 3) y = e* (x³ + 5) dy dy dx = e dx y = x° (In x + 2) y = e2* (5x + 3) dy dx dy = e dx

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Q2 - Stationary points
dy
dy
if y = x e*
Find
if y = x Inx
Find
dx
dx
dy
dy
e
dx
dx
Find the value of x
Find the value of x
at the stationary point. x =
at the stationary point. x =
d²y
Find a formula for
dx?
d'y
Find a formula for
dx?
d²y
d?y
e
dx²
dx?
Hence this is a
Hence this is a
min
max
min
max
Transcribed Image Text:Q2 - Stationary points dy dy if y = x e* Find if y = x Inx Find dx dx dy dy e dx dx Find the value of x Find the value of x at the stationary point. x = at the stationary point. x = d²y Find a formula for dx? d'y Find a formula for dx? d²y d?y e dx² dx? Hence this is a Hence this is a min max min max
Differentiate these using the product rule.
Write your answers in fully factorised form
with the common factor before the brackets.
y = x (x² + 3)
y = e* (x+ 5)
dy
dy
= e
dx
dx
y = x° (In x + 2)
y = e2* (5x + 3)
dy
dx
dy
= e
dx
)
3
y = x5e4x
y = 4x(x² - 2)
dy
dy
e
dx
dx
II
Transcribed Image Text:Differentiate these using the product rule. Write your answers in fully factorised form with the common factor before the brackets. y = x (x² + 3) y = e* (x+ 5) dy dy = e dx dx y = x° (In x + 2) y = e2* (5x + 3) dy dx dy = e dx ) 3 y = x5e4x y = 4x(x² - 2) dy dy e dx dx II
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