   Chapter 2.9, Problem 12E

Chapter
Section
Textbook Problem

# 11-14 Find the differential dy of each function.(a) y = 1 + 2 u 1 + 3 u (b) y = θ 2 sin 2 θ

To determine

a)

To find: The differential of dy

Explanation

1) Formula:

i.

ddxuv= v*dudx-u*dvdxv2

ii.

ddxxn=nxn-1

iii.

ddxaxn=a*nxn-1

iv.

ddxu+v=ddxu+ddx(v)

2) Given:

y=1+2u1+3u

3) Calculation:

Consider the given function

y=1+2u1+3u

Take the derivative with respect to u on both sides

dduy=ddu(1+2u1+3u)

By applying the quotient rule of differentiation,

ddxuv= v*dudx-u*dvdxv2

dydu=1+3u*ddu1+2u-1+2u*ddu(1+3u)1+3u2

=1

To determine

b)

To find: The differential of y

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