Derivatives

Higher Order Derivatives

When we just keep taking DERIVATIVES!

What are higher order derivatives?

• When you continue to take the derivative of a function!

• Each iteration uses the power rule

• You can take derivatives infinitely!

Multiple Choice

Find the second derivative of the following functions with respect to x.
y=3x²+5x-1

• 6x+5
• 3x+5
• 5
• 6

Multiple Choice

Find the second derivative of the function:

f (x) = 2x - 5x⁶

• f ''(x)= 2 - 30x

• f ''(x) = 2-30x⁵

• f ''(x) = -30x⁵

• f ''(x) = -150x⁴

Multiple Choice

Find f "'(x) when

f(x)=10x⁵ +3x⁴ -5x³ +2x² -10x+6

• 200x³+36x² -30x+4

• 600x² +72x -26

• 600x² +72x -30

• 600x² +72x -36

Multiple Choice

Find the 2nd derivative of f(x) = ¾x^½

• 3/4x^-3/2

• ⅛x^-½

• -1/16x^-½

• -1/16x^-3/2

Multiple Choice

Find the second derivative of the following functions with respect to x.

y=(x³+x)/x²

• x+(1/x)

• 1-(1/x²)

• 2/x²

• 2/x³

Multiple Choice

Find the second derivative of the following functions with respect to x.

y=(3x+2)¹⁰

• 10(3x+2)⁹

• 30(3x+2)⁹

• 810(3x+2)⁸

• 270(3x+2)⁸

Sometimes...

You have to use the rules more than once to take the second derivative!

This is espcially true with chain rule problems!