Question

If
f(x)=x^8+3x^3+3x

find the second derivative f"(x) .

I need starting to find just the first derivative.

Answer 1

The derivative of x^n is nx^(n-1). Apply this formula for each term in
f(x)=x^8+3x^3+3x and you will get the first derivative. Do it again and you will get your second derivative.

Answer 2

with the 3x using the nx^(n-1) would it just 8x^7+(3)3x^2+(1)3? or +(1)3x? @ranga

Answer 3

Your first two terms are correct.
But what is the derivative of 3x?
First let us find the derivative of x using the formula derivative of x^n is nx^(n-1)
x = x^1
So derivative of x^1 = (1)x^(1-1) = (1)x^0 = 1
So derivative of 3x = 3

Answer 4

Makes sense...so it's 8x^6+6x^2+3 correct? And then you use the same formula again so would it be (before multiplying) (7)8x^6+(2)6x+3?

Answer 5

Oh, you are already on to the second derivative.
But first simplify the first derivative:
f'(x) = 8x^7 + (3)3x^2 + 3
f'(x) = 8x^7 + 9x^2 + 3
f''(x) = ?
(Note derivative of a constant is 0).

Answer 6

So would it be 56x^6+18x?

Answer 7

Good!

Answer 8

Thank you so much! :)

Answer 9

You are welcome. Best wishes.