CALC BC- Derivatives

calculus

Average Rate of Change

Slope (f(b)-f(a))/(b-a)

Instantaneous Rate of Change

as the limit approaches c, (f(x)-f©)/(f-c)

Limit Definition of the Derivative

As the limit of h approaches 0, (f(x+h)-f(x))/h

sin²x+cos²x

=1

sin(x+y)

=sinxcosy+cosxsiny

cos(x+y)

cosxcosy-sinxsiny

Tangent Line of a graph of f at x=c

y-f©=f’©(x-c)

A line normal (perpendicular) to the graph of f at x=c

y-f©=(-1/f’©)(x-c)

Derivative of a Constant

0

Power Rule—→ x^n=

nx^(n-1)

Exponential Base e^x=

e^x

Logarithmic base lnx=

1/x

Derivative of sinx=

cosx

Derivative of tanx

sec²x

Derivative of secx

secxtanx

Derivative of cosx

-sinx

Derivative of cotx

-csc²x

Derivative of cscx

-cscxcotx