Derivative Basics

A derivative is the same as (equal to)

• slope of the original line

• slope of the tangent line

• slope of the secant line

• an integral

When we take the derivative of a function we are finding the slope of the ____________ line.

What is the derivative of xⁿ?

• (n-1)xⁿ
• nxⁿ⁺¹
• (n+1)x^n-1
• nx^n-1

What is the derivative of a constant?

• x

• 1

• 0

• What's a constant??

What rule would we use to find the derivative of this function f(x)=3x²tan(x)

• Sum Rule

• Power Rule

• Chain Rule

• Product Rule

Find the slope at x = 3 of the equation f(x) = 3x²

• 6x

• 27

• 18

• 3x

Differentiate y= x³ + 2x

• 3x³+2x
• 3x²+2
• 3x+2
• 3x

What rule would we use to find the derivative of this function f(x) = (5x⁵ + 5)²

• Quotient Rule

• Power Rule

• Chain Rule

• Product Rule

What is the derivative of e^x?

• xe^x

• e^x

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