# What is the derivative of the following funct ion? (1) y=4sin^-1(3×) (2) y=ln(5×+sin^-1(×) (3) y=3cos(sin^-1(2×+3))

##### 2 Answers

#### Explanation:

According to the chain rule,

Here, we have:

But since

Use the chain rule:

As

1)

2)

3)

#### Explanation:

You can Solve this Using the Chain Rule

basically,

which is the derivative of the first function(

multiplied by the derivative of

therefore for the first question,

let

and

therefore, for the derivative of

derivative of f(x) is

and of g(x) Is 3

therefore , the total derivative is

2)

similarly, for the second one,

derivative of

is

therefore the total derivative is

3)

use the same chain rule twice.

the derivative of the outside function =

which has to be evaluated at the inside function,

And the derivative of the inside function found using the chain rule is

therefore,

but since

the entire derivative is

And That's it