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

The derivative of (5x^3+5(x^4-3x)) is 35x^6-40x^3-15

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

The first derivative of (5x^3+5(x^4-3x)) is 35x^6-40x^3-15

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

35 x^{6} - 40 x^{3} - 15

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (5 x^{3} + 5) = 15 x^{2}

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

= 15 x^{2} (x^{4} - 3 x) + (4 x^{3} - 3) (5 x^{3} + 5)

Simplify

15 x^{2} (x^{4} - 3 x) + (4 x^{3} - 3) (5 x^{3} + 5) : 35 x^{6} - 40 x^{3} - 15

= 35 x^{6} - 40 x^{3} - 15

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What is the derivative of (5x^3+5(x^4-3x)) ?
The derivative of (5x^3+5(x^4-3x)) is 35x^6-40x^3-15
What is the first derivative of (5x^3+5(x^4-3x)) ?
The first derivative of (5x^3+5(x^4-3x)) is 35x^6-40x^3-15