To determine

To find: P'2

Answer

P'2=-2

Explanation

By differentiating and using values from the graph

1) Formula:

i. Sum rule:

ddxfx+gx=ddxfx+ddxg(x)

ii. Difference rule:

ddxfx-gx=ddxfx-ddxg(x)

iii. Product rule:

ddxfx.gx=fxddxgx+gxddxfx

iv. Chain rule:

ddx(fgx=f'gx*g'(x)

2) Given:

Px=fxgx

3) Calculation:

By using product rule,

P'(x)=ddx[fxgx]

ddx[fx.g(x)]=f(x)g'x+g(x)f'(x)

At x=2

P'2=f2g'2+g2f'2

From graph,

g'2=2 andf'2=-1

P'2=1*g'2+4*f'2=1*2+4*-1=2-4=-2

Conclusion:

Therefore, P'2=-2

To determine

To find: Q'2

Answer

Q'2=-38

Explanation

By differentiating and using values from the graph

1) Formula:

Quotient rule:

ddxfxgx= gxddxfx-fxddx(gx)gx2

2) Given:

Qx=fxgx

3) Calculation:

By using quotient rule,

Q'x=ddxfxgx=gxf'x-fxg'(x)gx2

At x=2 using values from the graph

Q'2=g2f'2-f2g'(2)g22=4*f'(2)-1*g'(2)16=4*(-1)-1*216=-616=-38

Conclusion:

Therefore,

Q'2=-38

To determine

To find:C'(2)

Answer

C'2=6

Explanation

Bydifferentiating and using values from the graph

Formula:

Chain rule:

ddx(fgx=f'gx*g'(x)

Given:

Cx=gx

Calculation:

By using chain rule,

C'(x)=ddx[f(gx)]

ddxfgx=f'gx.g'(x)

At x=2 using values from the graph

C'2=f'g2.g'2=f'g2.g'2=f'4*2=3*2=6

Conclusion:

Therefore,  C'2=6