calculate d/dx f(g(x)) is f(x)= 8x^3+5x^2-7 and g(x)= 2x+7

You substitute g(x) into the equation for f(x) in place of x

for f(x)= 8x

^{3}+ 5x^{2}- 7 and g(x)= 2x+7F(g(x)) = 8(2x+7)

^{3}+ 5(2x+7)^{2}- 7d/dx 8(2x+7)

^{3}+ 5(2x+7)^{2}- 7differentiate the sum term by term and factor out constants

d/dx(-7) + 5[ d/dx( (7+2x)

^{2})] + 8[ d/dx( (7+2x)^{3})]derivative of 7 is zero, simplify

5[ d/dx( (7+2x)

^{2})] + 8[ d/dx( (7+2x)^{3})]use the chain rule where

d/dx( (7+2x)

^{2}) = du^{2}/du(du/dx) , u = 2x+7 , d/du(u^{2}) = 2u5[ 2(2x+7) d/dx(7+2x)] + 8[ d/dx( (7+2x)

^{3})]Simplify

10(7+2x) [ d/dx (7+2x)] + 8[ d/dx( (7+2x)

^{3})]differentiate the sum term by term and factor out constants

10(2x+7) [ d/dx(7) +2
d/dx(x) ] + 8[ d/dx( (7+2x)

^{3})]derivative of 7 is zero , derivative of x is 1, simplify

20(2x+7) + 8[ d/dx( (7+2x)

^{3})]use the chain rule where

d/dx( (2x+7)

d/dx( (2x+7)

^{3}) = du^{3}/du(du/dx) , u = 2x+7 , d/du(u^{3}) = 3u^{2}20(2x+7) + 8( 3(2x+7)

^{2}[ d/dx( (7+2x)]simplify, and differentiate the sum term by term and factor out constants

20(2x+7) + 24(2x+7)

^{2}[ d/dx(7) + 2d/dx(x) ]derivative of 7 is 0, derivative of x is 1, simplify x2

20(2x+7) + 48(2x+7)

^{2}
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