Question

if f(x) +x^5[f(x)]^3=4005 and f(2) = 5, find f'(2)=

Answer 1

\[f'(x)+5x^4 \cdot [f(x)]^3+x^5 \cdot 3[f(x)]^2 f'(x)=0\]
now plug in x=2

Answer 2

and solve for f'(2)

Answer 3

\[f'(2)+5(2)^4 \cdot [f(2)]^3+2^5 \cdot 3 [f(2)]^2 f'(2)=0\]
\[f'(2)+f'(2) \cdot 2^5 \cdot 3 [f(2)]^2=-5(2)^4 \cdot[f(2)]^3\]
\[f'(2)[1+2^5 \cdot 3 [f(2)]^2=-5(2)^4 \cdot [f(2)]^3\]

Answer 4

\[f'(2)[1+2^5 \cdot 3 [f(2)]^2]=-5(2)^4 \cdot [f(2)]^3*\]

Answer 5

\[f'(2)[1+96[5]^2]=-80[5]^3\]

Answer 6

\[f'(2)[1+96(25)]=-80[125]\]
you got it from here?

Answer 7

what am i suppose to do with that?

Answer 8

solve for f'(2)

Answer 9

divde both sides by [1+96(25)]

Answer 10

i got -4.16 but it was wrong

Answer 11

\[\frac{-10000}{2401}\]

Answer 12

lol thankss