How do you find the derivative of #F(x)=arcsin sqrt sinx#?
2 Answers
Use the chain rule to find the derivative, because your function
Explanation:
The chain rule states that the derivative of a composite function is equal to the derivative of the individual composite functions with respect to their inner functions multiplied by the inner functions derivative with respect to x.
So
Since
And
And
Thus the derivative becomes
Simplifying, we get
This answer can be further simplified using trigonometric identities.
Explanation:
Take sines of both sides:
Implicit differentiation wrt x#:
Re-arrange:
Now draw a right-angled triangle and you will see that: