Chain Rule Checkpoint

h(x)=f(g(x))

h'(x)=?

• 1

• x

• f'(g(x)) x g'(x)

• f'(g'(x))

Tags

CCSS.HSF-BF.A.1C

How many derivatives do you have to know for h',

when h=f(g(x))

y=(x^2+3x)^4

y'=?

• 3(x^2+3x)^3

• 4x^2+12x

• 4(2x+3)^3

• 4(x^2+3x)^3 x (2x+3)

y=e^sinx

y'=?

• cosx(e^sinx)

• e^sinx

• cosx

• sinx(e^sinx)

h(x)=(f(x)/g(x))^2

h'(x)=?

• 2(f'/g')

• 2(f/g) x ((f'g)-(fg')/g^2)

y=3(x^4+5x^3+1)^2

• 6x^4+30x^3+6

• 3(4x^3+15x^2)^2

• 6(x^4+5x^3+1) x (x^4+5x^3+1)

• 6(x^4+5x^3+1) x (4x^3+15x^2)

h=sinx+e^3

h'(x)=?

• -cosx

• -cosx+e^3

• sinx+3e^3

• cosx

Tags

CCSS.HSF-BF.B.4A

y=f(g(f(f)))

y'=?

• f'(g(f(f)))g'(f(f))f'(f)f'

• f'(g'(f'(f')))

• f'(g)g'(f)f'(f)f'

• f'(f(g(f)))f'(g(f))g'

Tags

CCSS.HSF-BF.A.1C

y=9(x^3)^2

• 18(3x^2)

• 9(x^3)(3x^2)

• 9(3x^2)^2

• 18(x^3)(3x^2)

f(x)=(x^2+3x)/(4x+5)

f'(x)=?

1=top 2=bottom

• ((1'x2)-(1x2'))/(2')^2

• ((1'x2)-(1x2'))/(2)^2

Tags

CCSS.HSA.APR.D.6