What is the derivative of (8x^2+3x+1)*0.2x ?

The derivative of (8x^2+3x+1)*0.2x is 0.2(24x^2+6x+1)

What is the first derivative of (8x^2+3x+1)*0.2x ?

The first derivative of (8x^2+3x+1)*0.2x is 0.2(24x^2+6x+1)

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derivative of

(8 x^{2} + 3 x + 1) \cdot 0.2 x

0.2 (24 x^{2} + 6 x + 1)

Solution steps

\frac{d}{d x} ((8 x^{2} + 3 x + 1) \cdot 0.2 x)

Take the constant out:

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

= 0.2 \frac{d}{d x} ((8 x^{2} + 3 x + 1) x)

Apply the Product Rule:

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

f = 8 x^{2} + 3 x + 1, g = x

= 0.2 (\frac{d}{d x} (8 x^{2} + 3 x + 1) x + \frac{d x}{d x} (8 x^{2} + 3 x + 1))

\frac{d}{d x} (8 x^{2} + 3 x + 1) = 16 x + 3

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

= 0.2 ((16 x + 3) x + 1 \cdot (8 x^{2} + 3 x + 1))

Simplify

0.2 ((16 x + 3) x + 1 \cdot (8 x^{2} + 3 x + 1)) : 0.2 (24 x^{2} + 6 x + 1)

= 0.2 (24 x^{2} + 6 x + 1)

What is the derivative of (8x^2+3x+1)*0.2x ?
The derivative of (8x^2+3x+1)*0.2x is 0.2(24x^2+6x+1)
What is the first derivative of (8x^2+3x+1)*0.2x ?
The first derivative of (8x^2+3x+1)*0.2x is 0.2(24x^2+6x+1)