Prove by induction the first derivative

[scarlettjazz]

Hi, I'm stuck on this question:

Prove by mathematical induction that if y = x^n, then dy/dx= = nx^n-1. You may assume the product rule of differentiation.

I don't know where to start, and I don't know how to prove something by induction if it is not a series question.

You can also find the question in the HL maths textbook pg 620 review set 20B Q11.

For your reference, the product rule is: where y=uv, dy/dx = u(dv/dx) + v(du/dx)

Thanks for all of your help!

[dessskris]

you're a HL student so I assume you're capable of doing the math, but you just need some guidance on where to start.

okay so when n=1, y=x^1 or y=x. you differentiate it (find dy/dx) and then just mention that dy/dx=x^0=1 (which is true in this case)

then assume that when n=k, for y=x^k, then dy/dx=kx^(k-1).

when n=k+1, differentiate y=x^(k+1) by using your assumption, using product rule. you'll then get dy/dx=(k+1)x^k (or at least I hope so!)

don't forget to write the conclusion statement.

good luck with it! if you need further help let me know.