What is the derivative of (10x-2x^2(16-2x)) ?

The derivative of (10x-2x^2(16-2x)) is 12x^2-104x+160

What is the first derivative of (10x-2x^2(16-2x)) ?

The first derivative of (10x-2x^2(16-2x)) is 12x^2-104x+160

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\frac{d}{d x} ((10 x - 2 x^{2}) (16 - 2 x))

12 x^{2} - 104 x + 160

Solution steps

\frac{d}{d x} ((10 x - 2 x^{2}) (16 - 2 x))

Apply the Product Rule:

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

f = 10 x - 2 x^{2}, g = 16 - 2 x

= \frac{d}{d x} (10 x - 2 x^{2}) (16 - 2 x) + \frac{d}{d x} (16 - 2 x) (10 x - 2 x^{2})

\frac{d}{d x} (10 x - 2 x^{2}) = 10 - 4 x

\frac{d}{d x} (16 - 2 x) = - 2

= (10 - 4 x) (16 - 2 x) + (- 2) (10 x - 2 x^{2})

Simplify

(10 - 4 x) (16 - 2 x) + (- 2) (10 x - 2 x^{2}) : 12 x^{2} - 104 x + 160

= 12 x^{2} - 104 x + 160

What is the derivative of (10x-2x^2(16-2x)) ?
The derivative of (10x-2x^2(16-2x)) is 12x^2-104x+160
What is the first derivative of (10x-2x^2(16-2x)) ?
The first derivative of (10x-2x^2(16-2x)) is 12x^2-104x+160