What is the derivative of 9x(2x^2+1) ?

The derivative of 9x(2x^2+1) is 9(6x^2+1)

What is the first derivative of 9x(2x^2+1) ?

The first derivative of 9x(2x^2+1) is 9(6x^2+1)

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derivative of

9 x (2 x^{2} + 1)

9 (6 x^{2} + 1)

Solution steps

\frac{d}{d x} (9 x (2 x^{2} + 1))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 9 \frac{d}{d x} (x (2 x^{2} + 1))

Apply the Product Rule:

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

f = x, g = 2 x^{2} + 1

= 9 (\frac{d x}{d x} (2 x^{2} + 1) + \frac{d}{d x} (2 x^{2} + 1) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (2 x^{2} + 1) = 4 x

= 9 (1 \cdot (2 x^{2} + 1) + 4 xx)

Simplify

9 (1 \cdot (2 x^{2} + 1) + 4 xx) : 9 (6 x^{2} + 1)

= 9 (6 x^{2} + 1)

What is the derivative of 9x(2x^2+1) ?
The derivative of 9x(2x^2+1) is 9(6x^2+1)
What is the first derivative of 9x(2x^2+1) ?
The first derivative of 9x(2x^2+1) is 9(6x^2+1)