math induction question (1 Viewer)

[onebytwo]

we recently started MI and im having trouble with this question:
prove by MI:

d/dx (x^n) = nx^(n-1)

thanks in advance

 

[Riviet]

Hint:

Spoiler

Use the product rule before using your assumption

 

[onebytwo]

huhhhhh?
sorry, i dont get you!

 

[Riviet]

Assume d/dx(x^k)=kx^k-1
We are required to prove d/dx(x^k+1)=(k+1)x^k

LHS=d/dx(x^k+1)

=d/dx(x^k.x)

=x^k.1 + x.d/dx(x^k), by the product rule

=x^k + x(kx^k-1), by assumption

=x^k + kx^k

=(k+1)x^k

=RHS.

 

[onebytwo]

cool, i get it, thanks for the help