Differentiate g(x)=(x^2+1)^3*(7x+2)^2.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function g(x)=(x^2+1)^3*(7x+2)^2

g'(x)=[(x^2+1)^3(7x+2)^2]'

Use the product rule.

=> g'(x) = 2x*(x^2 + 1)^2*(7x + 2)^2 + (x^2 + 1)^3*2*7*(7x + 2)

=> g'(x) = 2x*(x^2 + 1)^2*(7x + 2)^2 + 14*(x^2 + 1)^3*(7x + 2)

=> 2*(x^2 + 1)^2*(7x + 2)(x*(7x + 2)^2 + 7*(x^2 + 1))

The derivative of g(x)=(x^2+1)^3*(7x+2)^2 is 2*(x^2 + 1)^2*(7x + 2)(x*(7x + 2)^2 + 7*(x^2 + 1))

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