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Popular >

derivative of (4x^3+5(x^4-2x))

Solution

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

Solution

28 x^{6} - 12 x^{3} - 10

Solution steps

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

Apply the Product Rule:

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

f = 4 x^{3} + 5, g = x^{4} - 2 x

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

\frac{d}{d x} (4 x^{3} + 5) = 12 x^{2}

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

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

Simplify

12 x^{2} (x^{4} - 2 x) + (4 x^{3} - 2) (4 x^{3} + 5) : 28 x^{6} - 12 x^{3} - 10

= 28 x^{6} - 12 x^{3} - 10

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (4x^3+5(x^4-2x)) ?
The derivative of (4x^3+5(x^4-2x)) is 28x^6-12x^3-10
What is the first derivative of (4x^3+5(x^4-2x)) ?
The first derivative of (4x^3+5(x^4-2x)) is 28x^6-12x^3-10