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

The derivative of (x^3+2^2(x^4+4)^4) is 6x^2(x^3+2)(x^4+4)^4+16x^3(x^4+4)^3(x^3+2)^2

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

The first derivative of (x^3+2^2(x^4+4)^4) is 6x^2(x^3+2)(x^4+4)^4+16x^3(x^4+4)^3(x^3+2)^2

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\frac{d}{d x} ((x^{3} + 2)^{2} (x^{4} + 4)^{4})

6 x^{2} (x^{3} + 2) (x^{4} + 4)^{4} + 16 x^{3} (x^{4} + 4)^{3} (x^{3} + 2)^{2}

Solution steps

\frac{d}{d x} ((x^{3} + 2)^{2} (x^{4} + 4)^{4})

Apply the Product Rule:

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

f = (x^{3} + 2)^{2}, g = (x^{4} + 4)^{4}

= \frac{d}{d x} ((x^{3} + 2)^{2}) (x^{4} + 4)^{4} + \frac{d}{d x} ((x^{4} + 4)^{4}) (x^{3} + 2)^{2}

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

\frac{d}{d x} ((x^{4} + 4)^{4}) = 16 x^{3} (x^{4} + 4)^{3}

= 6 x^{2} (x^{3} + 2) (x^{4} + 4)^{4} + 16 x^{3} (x^{4} + 4)^{3} (x^{3} + 2)^{2}

y^{^{'}} (t) = 0.3 y \cdot (1 - \frac{y}{2500}) - \frac{y}{4}, y (0) = 600

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What is the derivative of (x^3+2^2(x^4+4)^4) ?
The derivative of (x^3+2^2(x^4+4)^4) is 6x^2(x^3+2)(x^4+4)^4+16x^3(x^4+4)^3(x^3+2)^2
What is the first derivative of (x^3+2^2(x^4+4)^4) ?
The first derivative of (x^3+2^2(x^4+4)^4) is 6x^2(x^3+2)(x^4+4)^4+16x^3(x^4+4)^3(x^3+2)^2