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

The derivative of (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 (x^2+1^3(x^2+2)^6) ?

The first derivative of (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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\frac{d}{d x} ((x^{2} + 1)^{3} (x^{2} + 2)^{6})

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}

\int_{2}^{3} \frac{14}{3 - x} d x

\int \frac{1}{( x - 3 ) ^{\frac{3}{2}}} d x

x \to 0 lim (\frac{2 x + 1}{x ^{3}})

e^{e^{x} + x}

\frac{4}{2 x + 3}

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