What is the derivative of (3x^2-6x+10(x^3)) ?

The derivative of (3x^2-6x+10(x^3)) is 15x^4-24x^3+30x^2

What is the first derivative of (3x^2-6x+10(x^3)) ?

The first derivative of (3x^2-6x+10(x^3)) is 15x^4-24x^3+30x^2

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\frac{d}{d x} ((3 x^{2} - 6 x + 10) (x^{3}))

15 x^{4} - 24 x^{3} + 30 x^{2}

Solution steps

\frac{d}{d x} ((3 x^{2} - 6 x + 10) (x^{3}))

Apply the Product Rule:

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

f = 3 x^{2} - 6 x + 10, g = x^{3}

= \frac{d}{d x} (3 x^{2} - 6 x + 10) x^{3} + \frac{d}{d x} (x^{3}) (3 x^{2} - 6 x + 10)

\frac{d}{d x} (3 x^{2} - 6 x + 10) = 6 x - 6

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

= (6 x - 6) x^{3} + 3 x^{2} (3 x^{2} - 6 x + 10)

Simplify

(6 x - 6) x^{3} + 3 x^{2} (3 x^{2} - 6 x + 10) : 15 x^{4} - 24 x^{3} + 30 x^{2}

= 15 x^{4} - 24 x^{3} + 30 x^{2}

What is the derivative of (3x^2-6x+10(x^3)) ?
The derivative of (3x^2-6x+10(x^3)) is 15x^4-24x^3+30x^2
What is the first derivative of (3x^2-6x+10(x^3)) ?
The first derivative of (3x^2-6x+10(x^3)) is 15x^4-24x^3+30x^2