What is the derivative of (3x^4+4x^2(5x+8)^4) ?

The derivative of (3x^4+4x^2(5x+8)^4) is 2(3x^4+4x)(12x^3+4)(5x+8)^4+20(5x+8)^3(3x^4+4x)^2

What is the first derivative of (3x^4+4x^2(5x+8)^4) ?

The first derivative of (3x^4+4x^2(5x+8)^4) is 2(3x^4+4x)(12x^3+4)(5x+8)^4+20(5x+8)^3(3x^4+4x)^2

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\frac{d}{d x} ((3 x^{4} + 4 x)^{2} (5 x + 8)^{4})

2 (3 x^{4} + 4 x) (12 x^{3} + 4) (5 x + 8)^{4} + 20 (5 x + 8)^{3} (3 x^{4} + 4 x)^{2}

Solution steps

\frac{d}{d x} ((3 x^{4} + 4 x)^{2} (5 x + 8)^{4})

Apply the Product Rule:

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

f = (3 x^{4} + 4 x)^{2}, g = (5 x + 8)^{4}

= \frac{d}{d x} ((3 x^{4} + 4 x)^{2}) (5 x + 8)^{4} + \frac{d}{d x} ((5 x + 8)^{4}) (3 x^{4} + 4 x)^{2}

\frac{d}{d x} ((3 x^{4} + 4 x)^{2}) = 2 (3 x^{4} + 4 x) (12 x^{3} + 4)

\frac{d}{d x} ((5 x + 8)^{4}) = 20 (5 x + 8)^{3}

= 2 (3 x^{4} + 4 x) (12 x^{3} + 4) (5 x + 8)^{4} + 20 (5 x + 8)^{3} (3 x^{4} + 4 x)^{2}

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What is the derivative of (3x^4+4x^2(5x+8)^4) ?
The derivative of (3x^4+4x^2(5x+8)^4) is 2(3x^4+4x)(12x^3+4)(5x+8)^4+20(5x+8)^3(3x^4+4x)^2
What is the first derivative of (3x^4+4x^2(5x+8)^4) ?
The first derivative of (3x^4+4x^2(5x+8)^4) is 2(3x^4+4x)(12x^3+4)(5x+8)^4+20(5x+8)^3(3x^4+4x)^2