Ch 17: Inverse Derivative, Inverse Derivative of Trig Functions, Inverse Derivative of Trigonometric Functions

what is the formula for the derivative of the inverse

what is the derivative of what is arcsinx

what is the derivative of arctanx

what is the derivative of arcsecx

what is the derivative of arccosx

what is the derivative of arccotx

what is the derivative of arccscx

How do you find the derivative of an inverse trig function?

(inverse of trig function (make sure “x” matches**)) * derivative of “x”

ex:

How to use chain rule when its a^{(trig function)}

keep it the same * ln(a) * (trig function)’z

ex:

d/dx[ln(x)] =

1/x

d/dx[log_b(x)] =

1/(x*ln(b))

d/dx[ln(g(x))] =

g’(x) / g(x)

d/dx[ln(u)] =

(1/u) * (u’)

how do you do chain rule when there a 3 functions?

1. take derivative of outside-outside function

2. take derivative of middle function

3. take derivative of inside-inside function
   

   ex:

steps of logarithmic differentiation

1. Use law of logs to expand the equation

2. Take ln of both sides

3. differentiate

4. solve for y’

5. Plug in OG y

For a,b constants
d/dx (a^b) =

0

For a,b constants
d/dx ([f(x)]^b) =

bf(x)^b-1 * f’(x)

For a,b constants
d/dx (a^g(x)) =

a^g(x) * ln(a) * g’(x)

For a,b constants
d/dx ([f(x)]^g(x)]

logarithmic differentiation