Thread: 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?

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?







surely, you have been already taught about these..

Originally Posted by lemontea

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

Find dy/dx by implicit differentation

so, let

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 ?

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