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

The derivative of (x^2+2^2(x^2+2x+1)^3) is 4x(x^2+2)(x^2+2x+1)^3+3(x^2+2x+1)^2(2x+2)(x^2+2)^2

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

The first derivative of (x^2+2^2(x^2+2x+1)^3) is 4x(x^2+2)(x^2+2x+1)^3+3(x^2+2x+1)^2(2x+2)(x^2+2)^2

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

4 x (x^{2} + 2) (x^{2} + 2 x + 1)^{3} + 3 (x^{2} + 2 x + 1)^{2} (2 x + 2) (x^{2} + 2)^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((x^{2} + 2)^{2}) = 4 x (x^{2} + 2)

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

= 4 x (x^{2} + 2) (x^{2} + 2 x + 1)^{3} + 3 (x^{2} + 2 x + 1)^{2} (2 x + 2) (x^{2} + 2)^{2}

2 (12) (5) + 2 (5) \frac{d y}{d t} = 0

\int 11 cot^{4} (x) d x

\int x^{2} cos^{3} (x^{3}) sin^{2} (x^{3}) d x

\int_{1}^{e} \frac{( ln ( x ) ) ^{2}}{x} d x

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

What is the derivative of (x^2+2^2(x^2+2x+1)^3) ?
The derivative of (x^2+2^2(x^2+2x+1)^3) is 4x(x^2+2)(x^2+2x+1)^3+3(x^2+2x+1)^2(2x+2)(x^2+2)^2
What is the first derivative of (x^2+2^2(x^2+2x+1)^3) ?
The first derivative of (x^2+2^2(x^2+2x+1)^3) is 4x(x^2+2)(x^2+2x+1)^3+3(x^2+2x+1)^2(2x+2)(x^2+2)^2