   Chapter 2.3, Problem 27E

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# Differentiate. F ( y ) = ( 1 y 2 − 3 y 4 ) ( y + 5 y 3 )

To determine

To find:

Derivative of F(y)

Explanation

Formula:

Power rule,  ddxxn=nxn-1

Sum rule,  ddxfx+gx=ddx(fx+ddx(g(x)

Product rule,  ddxfx*gx= fx*ddx(gx+ gx*ddx(f(x)

Given:

Fy=1y2-3y4(y+5y3)

Calculation:

Consider the given function Fy=1y2-3y4(y+5y3)

Differentiate with respect to y on both sides to get

ddyFy= ddy(1y2-3y4y+5y3)

By applying the product rule of differentiation

F'y=y+5y3*ddy1y2-3y4+1y2-3y4*ddy(y+5y3)

Applying the sum rule of differentiation

F'(y)=y+5y3*ddy1y2-ddy3y

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