Differentiating 2^x (1 Viewer)

[foram]

y=2^x

Differentiating

(1st Method)

ln y = x . ln 2
1/y . dy/dx = ln2
dy/dx = y . ln2
dy/dx = 2^x . ln2 (answer)



(2nd Method)

y=2^x = e^x.ln 2
dy/dx = e^x.ln2 . ln2
dy/dx = 2^x . ln2 (answer)


Which method is better to use in a test?

 

[lyounamu]

Alttough it's great to know both

I think in an exam situation it might be best to use the meothd that has the least amount of working out involved....which would save time

Based on this, I would say method 2.

Agree with Trajan. I use the 2nd method. My teacher didn't teach us that since he thought it is not in the syllabus. But I taught it myself just in case that question suddenly arises in exam.

EDIT: YOU would get full marks for each one, anyway.

 

[Aerath]

I prefer the first method, because it's easier for me to understand.

 

[bored of sc]

what is differentiation??

 

[Continuum]

Finding the derivative, which is the gradient of the tangent at any point on the curve. It's represented either by y', f'(x) or dy/xy. I learnt it after learning about limits in the form of lim, so you should learn it about then.

 

[lyounamu]

dy/xyquote]
dy/dx

 

[Aerath]

what is differentiation??

If you haven't learnt it - don't worry about it. You'll learn it later on. There's really no point learning stuff ahead of time if you're not going to use it.

 

[The Kaiser]

Wow, I didn't know the actual working to these types of questions.

I always just use the simple method

(y= a^x) and dy/dx = a^x * log(e)a or lna

or y= log(a) x and dy/dx = 1/x*lna

 

[Continuum]

dy/xy

dy/dx

Oh... my bad.