Thread: Differentiating functions

I need help understanding how to differentiate functions, i have a few examples below, if you could help me understand that would be great.

y=3x²-5x+1

p=100- e³/6( sorry don't know how to format that correctly)

r=2ln(t/10)

the / is me showing it as a fraction, i dont know how to format it correctly

1) The derivative of af+ bg, where a and b are numbers and f and g are functions, is af'+ bg'. And the derivative of [itex]x^n[/itex], with respect to x, is [itex]nx^{n-}[/itex].

2) Same as (1). I presume you want to differentiate p with respect to e. And so I am assuming that "e" is NOT the base of the natural logarithm, a constant.

3) The derivative of ln(u), with respect to u, is 1/u. You also need the "chain rule": if f is a function of u and u is a function of t, df/dx= (df/du)(du/dt). Here, u= t/10.

Surely these "rules" are in our textbook?

It's hard to really get the feel for derivatives through text/reading.
I will be making videos shortly on derivatives, including logarithmic differentiation.
Please check out my new channel at robbiecee2 - YouTube

Just in case a picture helps anyone, youtubers included! ...



... where (key in spoiler) ...

Spoiler:

... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in these cases x or e or t), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

The general drift is...

_________________________________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!

^^ agreed, good idea.

Thanks. Careful you don't spam though - i.e. link without contributing (appropriately) to the thread.

Okay, thanks

thanks very much for your help, i am now going to try this with other examples

Im very new to maths and do not have an A level in it but doing economics at uni so gonna have to get to grips with it, so using summer to help me!