   Chapter 2.5, Problem 24E

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# Find the derivative of the function. U ( y ) = ( y 4 + 1 y 2 + 1 ) 5

To determine

To find:the derivative of Uy= y4+1y2+15

Explanation

Formula:

i. d(xy)dx=y.ddxx  -  x.ddx(y)y2

ii. d(xn)dx=nxn-1

Given:

Uy= y4+1y2+15

Calculation:

Let u= y4+1y2+1

Then Uu=u5

By using chain rule we can write

U'y=dduUu.ddy(u)

U'y=ddu(u5).ddyy4+1y2+1

By using power rule of derivative

U'y=5u4ddyy4+1y2+1

Now by using rule d(xy)dx=y.ddxx  -  x.ddx(y)y2

U'y=5u4(y2+1)ddy(y4+1)-y4+1ddx(y2+1)   y2+12

By using power rule

ddxy2+1=2y

ddxy4+1=4y3

Substitute this in U'y

U'y=5u4(y2+1).4y3- y4+1

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