What is the derivative of g(x)=(x^2+1)^3(x^2+2)^6 ?

The derivative of g(x)=(x^2+1)^3(x^2+2)^6 is 6x(x^2+1)^2(x^2+2)^6+12x(x^2+2)^5(x^2+1)^3

What is the first derivative of g(x)=(x^2+1)^3(x^2+2)^6 ?

The first derivative of g(x)=(x^2+1)^3(x^2+2)^6 is 6x(x^2+1)^2(x^2+2)^6+12x(x^2+2)^5(x^2+1)^3

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derivative

6 x (x^{2} + 1)^{2} (x^{2} + 2)^{6} + 12 x (x^{2} + 2)^{5} (x^{2} + 1)^{3}

Solution steps

\frac{d}{d x} ((x^{2} + 1)^{3} (x^{2} + 2)^{6})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (x^{2} + 1)^{3}, g = (x^{2} + 2)^{6}

= \frac{d}{d x} ((x^{2} + 1)^{3}) (x^{2} + 2)^{6} + \frac{d}{d x} ((x^{2} + 2)^{6}) (x^{2} + 1)^{3}

\frac{d}{d x} ((x^{2} + 1)^{3}) = 6 x (x^{2} + 1)^{2}

\frac{d}{d x} ((x^{2} + 2)^{6}) = 12 x (x^{2} + 2)^{5}

= 6 x (x^{2} + 1)^{2} (x^{2} + 2)^{6} + 12 x (x^{2} + 2)^{5} (x^{2} + 1)^{3}

What is the derivative of g(x)=(x^2+1)^3(x^2+2)^6 ?
The derivative of g(x)=(x^2+1)^3(x^2+2)^6 is 6x(x^2+1)^2(x^2+2)^6+12x(x^2+2)^5(x^2+1)^3
What is the first derivative of g(x)=(x^2+1)^3(x^2+2)^6 ?
The first derivative of g(x)=(x^2+1)^3(x^2+2)^6 is 6x(x^2+1)^2(x^2+2)^6+12x(x^2+2)^5(x^2+1)^3