Question

F(x) = (5x3 + 4)3 find the second derivative

Answer 1

step by step please

Answer 2

I assume that the 3 is a power?

Answer 3

well i used chain rule

Answer 4

f'(x)=3(5x3 + 4)^2[15x^2]

Answer 5

[45(x2)](2)(5x3 +4)1(15x3-1) + (45x2) (5x3 + 4)2

Answer 6

\[45(5x^3+4)(x^2)\]

Answer 7

oh again missed the exponent 2

Answer 8

is my first step corrrect

Answer 9

\[f'(x)=45(5x^3+4)^2(x^2)\]

Answer 10

(45x2) (5x3 + 4)2

Answer 11

3 is not in power?

Answer 12

right, now how to do second derivative

Answer 13

use product rule

Answer 14

F(x) = (5x^3 + 4)^2

Answer 15

is the questions

Answer 16

wait your derivative doesnt seem right

Answer 17

this is not the same u posted earlier

Answer 18

oh no
its to the third power

Answer 19

but the way you wrote the answer is different

Answer 20

(45x^2) (5x3 + 4)2 by using chain rule

Answer 21

then the derivative is correct:)

Answer 22

right

Answer 23

now use the product rule

Answer 24

you left the 45 and x^2 separately

Answer 25

confused me

Answer 26

y confused?

Answer 27

45(5x3+4)(x2)

Answer 28

how can you separate 45 from the equation

Answer 29

this is the second step, read the first too

Answer 30

y seperated? it is being multiplied

Answer 31

ok let me me work it out and see if our answers match

Answer 32

ok take ur time

Answer 33

(450x5 + 360 + 2250x10+3600x4 + 1440x)

Answer 34

whats that?

Answer 35

the expanded version of = (45x2) * 2(5x3 + 4) + 2(45x) * (5x3 + 4)2

Answer 36

(45x2) (5x3 + 4)2

Answer 37

became expanded version then that long ans

Answer 38

y did u expand it?

Answer 39

did u check the first derivative?

Answer 40

not supposed to?

Answer 41

but u were gonna do that

Answer 42

hmm.. first derivative = (45x2) (5x3 + 4)2

Answer 43

correct?

Answer 44

it has to be

Answer 45

used chain rule

Answer 46

f''(x)= 90x(5x3 + 4)^2+(45x^2)2(5x^3+4)15x^2

Answer 47

\[90x(5x^3+4)^2 + (675x^3)(5x^3+4)\]

Answer 48

where did u get 15x2 from

Answer 49

it was already simplified in the first derivative

Answer 50

= [(45x2) * 2(5x3 + 4)] + [90x * (5x3 + 4)2]

Answer 51

open that up = [(45x2) * (10x3 + 8)] + [90x * (25x9 + 40x3 + 16)]

Answer 52

open further = = 2250x10 + 450x5 + 3600x4 + 1440x

Answer 53

is that correct?

Answer 54

u know how to apply chain rule?

Answer 55

you said product rule i think thats where i made the mistake

Answer 56

chain rule is again used in product rule

Answer 57

ohhhh

Answer 58

alright let me solve again and brb

Answer 59

ok

Answer 60

[(45x2)*2(5x3 + 4)*15x2] + [90x * 90(5x3 + 4)2]