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Popular >

derivative of (3x^3+4(x^4-4x))

Solution

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

Solution

21 x^{6} - 32 x^{3} - 16

Solution steps

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

Apply the Product Rule:

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

f = 3 x^{3} + 4, g = x^{4} - 4 x

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

\frac{d}{d x} (3 x^{3} + 4) = 9 x^{2}

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

= 9 x^{2} (x^{4} - 4 x) + (4 x^{3} - 4) (3 x^{3} + 4)

Simplify

9 x^{2} (x^{4} - 4 x) + (4 x^{3} - 4) (3 x^{3} + 4) : 21 x^{6} - 32 x^{3} - 16

= 21 x^{6} - 32 x^{3} - 16

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (3x^3+4(x^4-4x)) ?
The derivative of (3x^3+4(x^4-4x)) is 21x^6-32x^3-16
What is the first derivative of (3x^3+4(x^4-4x)) ?
The first derivative of (3x^3+4(x^4-4x)) is 21x^6-32x^3-16