What is the derivative of (6x^3+2x+9)(x^2+6) ?

The derivative of (6x^3+2x+9)(x^2+6) is 30x^4+114x^2+18x+12

What is the first derivative of (6x^3+2x+9)(x^2+6) ?

The first derivative of (6x^3+2x+9)(x^2+6) is 30x^4+114x^2+18x+12

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derivative of

(6 x^{3} + 2 x + 9) (x^{2} + 6)

30 x^{4} + 114 x^{2} + 18 x + 12

Solution steps

\frac{d}{d x} ((6 x^{3} + 2 x + 9) (x^{2} + 6))

Apply the Product Rule:

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

f = 6 x^{3} + 2 x + 9, g = x^{2} + 6

= \frac{d}{d x} (6 x^{3} + 2 x + 9) (x^{2} + 6) + \frac{d}{d x} (x^{2} + 6) (6 x^{3} + 2 x + 9)

\frac{d}{d x} (6 x^{3} + 2 x + 9) = 18 x^{2} + 2

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

= (18 x^{2} + 2) (x^{2} + 6) + 2 x (6 x^{3} + 2 x + 9)

Simplify

(18 x^{2} + 2) (x^{2} + 6) + 2 x (6 x^{3} + 2 x + 9) : 30 x^{4} + 114 x^{2} + 18 x + 12

= 30 x^{4} + 114 x^{2} + 18 x + 12

What is the derivative of (6x^3+2x+9)(x^2+6) ?
The derivative of (6x^3+2x+9)(x^2+6) is 30x^4+114x^2+18x+12
What is the first derivative of (6x^3+2x+9)(x^2+6) ?
The first derivative of (6x^3+2x+9)(x^2+6) is 30x^4+114x^2+18x+12