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[SOLVED] s8.2.5.7 chain rule

karush

Well-known member
Jan 31, 2012
2,678
find $F'(x)$
$$F(x)=(7x^6+8x^3)^4$$
chain rule
$$4(7x^6+8x^3)^3(42x^5+24x^2)$$
factor
$$4x^3(7x^3+8)^3 6x^2(7x^3+4)$$

ok W|A returned this but dont see where the 11 came from
$$24 x^{11} (7 x^3 + 4) (7 x^3 + 8)^3$$
 

topsquark

Well-known member
MHB Math Helper
Aug 30, 2012
1,121
find $F'(x)$
$$F(x)=(7x^6+8x^3)^4$$
chain rule
$$4(7x^6+8x^3)^3(42x^5+24x^2)$$
factor
$$4x^3(7x^3+8)^3 6x^2(7x^3+4)$$

ok W|A returned this but dont see where the 11 came from
$$24 x^{11} (7 x^3 + 4) (7 x^3 + 8)^3$$
Look at your first factor:
\(\displaystyle \left ( 7x^6 + 8 x^3 \right ) ^3 = ( x^3 ( 7 x^3 + 8 ) )^3 = (x^3)^3 (7 x^3 + 8 )^3\)

Don't worry. It's an easy mistake to make and a pain in the pahtootie to find when you check your work.

-Dan
 

karush

Well-known member
Jan 31, 2012
2,678
yeah that was kinda behind the bushes....