Differentiation help! (1 Viewer)

[MissyL]

Given
y=ln⁡(e^x 〖sin〗^2 x)
Show that:
dy/dx=1+2cotx

Also
If y=secx
prove that dy/dx= secxtanx. I've been using the first principle thing the whole time, maybe I'm using it wrong or something, but help is much appreciated!

 

[SpiralFlex]

Not at home at the moment so don't have computer handy. I will explain further if you need

Hint 1: Can we perhaps change the form ln (ab) into ln a + ln b

Hint for 2: sec x we can change into our other more recognisable circular function in a fraction form. If you can do that then apply a differentiation rule

You can differentiate sec x via "first principles" via sum and products formulae but the above may be quicker

 

[MissyL]

Thanks! I got the second question! but not the first one haha...

 

[Carrotsticks]

Thanks! I got the second question! but not the first one haha...

Do you remember what the derivative of y=ln(f(x)) is?

 

[MissyL]

Do you remember what the derivative of y=ln(f(x)) is?

1/x times f'(x)?

 

[asianese]

Actually, if



then

 

[namelyanonymous]

1/x times f'(x)?

1/f(x) * f'(x) (differentiate with respect to f(x), then differentiate f(x) with respect to x)

 

[MissyL]

Actually, if



then

Oh okay, thanks!

 

[MissyL]

Thanks everyone!