   Chapter 2.R, Problem 23E

Chapter
Section
Textbook Problem

# 13–40 Calculate y ' . x y 4 + x 2 y = x + 3 y

To determine

To calculate:

y'

Explanation

Rule:

i. Power rule:

ddxxn=nxn-1

ii. Sum rule

ddxfx+g(x)=ddxfx+ddxgx

iii. Product rule:

uv'=vu'+uv'

iv. Constant multiple rule:

ddxcfx=c.ddxfx

Given:

xy4+x2y=x+3y

Calculation:

xy4+x2y=x+3y

Differentiate with respect to x

ddxxy4+x2y=ddxx+3y

By using sum rule

ddxxy4+ddx(x2y)=ddx(x)+ddx(3y)

By using product rule and constant multiple rule

y4.ddxx+x.ddx(y4)+y.ddxx2+x2.ddxy= ddx(x)+3ddx(y)

By using power rule and power rule combined with chain rule

y4

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