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

The derivative of (5x^2-2(x^3+3x)) is 25x^4+39x^2-6

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

The first derivative of (5x^2-2(x^3+3x)) is 25x^4+39x^2-6

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

25 x^{4} + 39 x^{2} - 6

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (5 x^{2} - 2) = 10 x

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

= 10 x (x^{3} + 3 x) + (3 x^{2} + 3) (5 x^{2} - 2)

Simplify

10 x (x^{3} + 3 x) + (3 x^{2} + 3) (5 x^{2} - 2) : 25 x^{4} + 39 x^{2} - 6

= 25 x^{4} + 39 x^{2} - 6

What is the derivative of (5x^2-2(x^3+3x)) ?
The derivative of (5x^2-2(x^3+3x)) is 25x^4+39x^2-6
What is the first derivative of (5x^2-2(x^3+3x)) ?
The first derivative of (5x^2-2(x^3+3x)) is 25x^4+39x^2-6