Question

Find the derivative.

f(x)=x^2(x^3+3x^2)

I got 120x+72. Anyone care to check my answer?

Answer 1

did you use product rule?

Answer 2

yea.

Answer 3

why can't we just distribute first?

Answer 4

i got something different

Answer 5

oh lol of course

Answer 6

What did you get Igbasallote?

Answer 7

just distribute...it's faster...youll get same answer anyway... \[\frac{d}{dx} (x^5) + \frac{d}{dx} (3x^2)\]

Answer 8

I did. I know how to do it, i just want to know where i did the mistake lol o_O

Answer 9

but if you prefer product rule... \[x^2 \frac{d}{dx} (x^3 + 3x^2) + (x^3 + 3x^2)\frac{d}{dx} (x^2)\]

Answer 10

derivative of x^5 is 5x^4 due to the power rule \(\frac{d}{dx}x^n = nx^{n-1}\)

Answer 11

continueeeee. I got 20x^3 after that.

Answer 12

btw that\s supposed to be \(\frac{d}{dx} (3x^4)\) not 3x^2

Answer 13

i mistyped

Answer 14

derivative of 3x^4 = \((3 \times 4)x^{4-1}\)

Answer 15

yea after that I got 5x^4+12x^3

Answer 16

^that's right

Answer 17

then 20x^3+36x^2

Answer 18

hello?

Answer 19

why

Answer 20

why did you make it 20x^3 + 36x^2?

Answer 21

because the exponent times 5 and then decrease the exponent by 1. So 5*4=20, then x^4-1=20x^3

Answer 22

and i did the same for the next number.

Answer 23

are you looking for second derivative?

Answer 24

I'm looking for the most simplified derivative possible.

Answer 25

that's as simplified you can get...if you take the derivative it's no longer equal

Answer 26

5x^4 + 12x^3 is enough

Answer 27

But I'm required to go further to find it until the 5th derivative. This is only the 2nd or 3rd.

Answer 28

oh..until 5th derivative?

well 2nd derivative = 20x^3 + 36x^2

3rd derivative = 60x^2 + 72x

4th derivative = 120 x + 72

5th = 120

Answer 29

Yup I got that for my 4th lol. Thanks. That's all I needed to know lol.