1. ## Trignometric functions derivative

Find the derivative of the function

1.) f(x)=sqrt(cosx+sinx)

f(x)= (cosx+sinx)^1/2
f'(x)= 1/2(cosx+sinx)^-1/2 d/dx (cosx+sinx)
= ???

2.) f(x)=e^(tanx+secx)
f'(x)=e^(tanx+secx) 。d/dx(tanx+secx)
=???

3.) f(x)= ln(sin^-1 (x))

Find dy/dx by implicit differentation

1.) x sec(y)=ln(sinx)

The text in the red is what i got so far..then i got stuck..can anyone help me?

2. Originally Posted by lemontea
Find the derivative of the function

1.) f(x)=sqrt(cosx+sinx)

f(x)= (cosx+sinx)^1/2
f'(x)= 1/2(cosx+sinx)^-1/2 d/dx (cosx+sinx)
= ???

2.) f(x)=e^(tanx+secx)
f'(x)=e^(tanx+secx) 。d/dx(tanx+secx)
=???
yes.. and how do you find the derivative of the sum?
$\displaystyle \frac{d}{dx}\sin x = ?$
$\displaystyle \frac{d}{dx}\cos x = ?$
$\displaystyle \frac{d}{dx}\tan x = ?$
$\displaystyle \frac{d}{dx}\csc x = ?$
$\displaystyle \frac{d}{dx}\sec x = ?$
$\displaystyle \frac{d}{dx}\cot x = ?$

Originally Posted by lemontea
3.) f(x)= ln(sin^-1 (x))

Find dy/dx by implicit differentation
so, let $\displaystyle y = \ln (\sin^{-1} x) \Longleftrightarrow e^y = \sin^{-1} x$

Originally Posted by lemontea
1.) x sec(y)=ln(sinx)

The text in the red is what i got so far..then i got stuck..can anyone help me?
do you already know $\displaystyle \frac{d}{dx}(\ln x)$?

3. Perhaps you might have forgotten to write it down in the lecture or the book doesn't mention it in any way Just have a look at this:
World Web Math: Rules of differentiation