Derivatives Of Inverse Trigonometric Functions Worksheet printable pdf download

Derivatives Of Inverse Trigonometric Functions Worksheet

DERIVATIVES OF INVERSE TRIGONOMETRIC FUNCTIONS

1. Implicit differentiation

In math 1, we learned about the function ln x being the inverse of the function

. Remember that we found the derivative of ln x by diﬀerentiating the equation

ln x = y.

First, you wrote it in terms of functions that we knew:

x = e

Then, we took the derivative of both sides

1 = e

Then, since e

= x, we simpliﬁed to

1 = x

and concluded by dividing both sides by x to get

2. Inverse trig functions

We will do the same for the inverse trig functions. The process is the same, it is

just a little hard to simplify.

Example 1. Find the

when y = Sin

(x).

Solution. Again we start by writing it in terms of functions we know better, so

sin(y) = x

for y ∈

. Now, take the derivative of both sides,

cos(y)

= 1.

Now y = Sin

(x) so we need to simplify cos(Sin

(x)). We did this in Example 5

of the previous packet where we showed

cos(Sin

(x)) =

So we conclude that

√

Derivatives Of Inverse Trigonometric Functions Worksheet