MTHSC 102 Section 3.2-3 – Simple Rate
of Change Formulas
Kevin James
Kevin James
MTHSC 102 Section 3.2-3 – Simple Rate of Change Formulas
Simple Derivative Rules
Rule Name
Function
Constant Rule
y =b
Kevin James
Derivative
dy
=0
dx
MTHSC 102 Section 3.2-3 – Simple Rate of Change Formulas
Simple Derivative Rules
Rule Name
Function
Constant Rule
Linear Function Rule
y =b
y = ax + b
Kevin James
Derivative
dy
=0
dx
dy
=a
dx
MTHSC 102 Section 3.2-3 – Simple Rate of Change Formulas
Simple Derivative Rules
Rule Name
Function
Constant Rule
Linear Function Rule
y =b
y = ax + b
y = xn
Power Rule
Kevin James
Derivative
dy
=0
dx
dy
=a
dx
dy
= nx n−1
dx
MTHSC 102 Section 3.2-3 – Simple Rate of Change Formulas
Simple Derivative Rules
Rule Name
Function
Constant Rule
y =b
Linear Function Rule
y = ax + b
y = xn
Power Rule
Constant Multiple Rule
y = kf (x)
Kevin James
Derivative
dy
=0
dx
dy
=a
dx
dy
= nx n−1
dx
dy
= kf 0 (x)
dx
MTHSC 102 Section 3.2-3 – Simple Rate of Change Formulas
Simple Derivative Rules
Rule Name
Function
Constant Rule
y =b
Linear Function Rule
y = ax + b
y = xn
Power Rule
Constant Multiple Rule
Sum Rule
y = kf (x)
y = f (x) + g (x)
Kevin James
Derivative
dy
=0
dx
dy
=a
dx
dy
= nx n−1
dx
dy
= kf 0 (x)
dx
dy
= f 0 (x) + g 0 (x)
dx
MTHSC 102 Section 3.2-3 – Simple Rate of Change Formulas
Simple Derivative Rules
Rule Name
Function
Constant Rule
y =b
Linear Function Rule
y = ax + b
y = xn
Power Rule
Constant Multiple Rule
y = kf (x)
Sum Rule
y = f (x) + g (x)
Difference Rule
y = f (x) − g (x)
Kevin James
Derivative
dy
=0
dx
dy
=a
dx
dy
= nx n−1
dx
dy
= kf 0 (x)
dx
dy
= f 0 (x) + g 0 (x)
dx
dy
= f 0 (x) − g 0 (x)
dx
MTHSC 102 Section 3.2-3 – Simple Rate of Change Formulas
Simple Derivative Rules
Rule Name
Function
Constant Rule
y =b
Linear Function Rule
y = ax + b
y = xn
Power Rule
Constant Multiple Rule
y = kf (x)
Sum Rule
y = f (x) + g (x)
Difference Rule
y = f (x) − g (x)
Exponential Rule
y = b x (b > 0)
Kevin James
Derivative
dy
=0
dx
dy
=a
dx
dy
= nx n−1
dx
dy
= kf 0 (x)
dx
dy
= f 0 (x) + g 0 (x)
dx
dy
= f 0 (x) − g 0 (x)
dx
dy
= (ln b)b x
dx
MTHSC 102 Section 3.2-3 – Simple Rate of Change Formulas
Simple Derivative Rules
Rule Name
Function
Constant Rule
y =b
Linear Function Rule
y = ax + b
y = xn
Power Rule
Constant Multiple Rule
y = kf (x)
Sum Rule
y = f (x) + g (x)
Difference Rule
y = f (x) − g (x)
Exponential Rule
y = b x (b > 0)
e x Rule
y = ex
Kevin James
Derivative
dy
=0
dx
dy
=a
dx
dy
= nx n−1
dx
dy
= kf 0 (x)
dx
dy
= f 0 (x) + g 0 (x)
dx
dy
= f 0 (x) − g 0 (x)
dx
dy
= (ln b)b x
dx
dy
= ex
dx
MTHSC 102 Section 3.2-3 – Simple Rate of Change Formulas
Simple Derivative Rules
Rule Name
Function
Constant Rule
y =b
Linear Function Rule
y = ax + b
y = xn
Power Rule
Constant Multiple Rule
y = kf (x)
Sum Rule
y = f (x) + g (x)
Difference Rule
y = f (x) − g (x)
Exponential Rule
y = b x (b > 0)
e x Rule
Natural Log Rule
y = ex
y = ln(x), (x > 0)
Kevin James
Derivative
dy
=0
dx
dy
=a
dx
dy
= nx n−1
dx
dy
= kf 0 (x)
dx
dy
= f 0 (x) + g 0 (x)
dx
dy
= f 0 (x) − g 0 (x)
dx
dy
= (ln b)b x
dx
dy
= ex
dx
dy
= x1
dx
MTHSC 102 Section 3.2-3 – Simple Rate of Change Formulas
Example
Suppose that f (x) = 3x 3 − 4x 2 + 3x + 5e x − 8 ln(x). Give a
formula for f 0 (x).
Kevin James
MTHSC 102 Section 3.2-3 – Simple Rate of Change Formulas