What is the derivative of (2x-84(x^2+x+1)5) ?

The derivative of (2x-84(x^2+x+1)5) is 20(6x^2-12x-6)

What is the first derivative of (2x-84(x^2+x+1)5) ?

The first derivative of (2x-84(x^2+x+1)5) is 20(6x^2-12x-6)

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\frac{d}{d x} ((2 x - 8) 4 (x^{2} + x + 1) 5)

20 (6 x^{2} - 12 x - 6)

Solution steps

\frac{d}{d x} ((2 x - 8) \cdot 4 (x^{2} + x + 1) \cdot 5)

Simplify

(2 x - 8) \cdot 4 (x^{2} + x + 1) \cdot 5 : 20 (2 x - 8) (x^{2} + x + 1)

= \frac{d}{d x} (20 (2 x - 8) (x^{2} + x + 1))

Take the constant out:

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

= 20 \frac{d}{d x} ((2 x - 8) (x^{2} + x + 1))

Apply the Product Rule:

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

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

= 20 (\frac{d}{d x} (2 x - 8) (x^{2} + x + 1) + \frac{d}{d x} (x^{2} + x + 1) (2 x - 8))

\frac{d}{d x} (2 x - 8) = 2

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

= 20 (2 (x^{2} + x + 1) + (2 x + 1) (2 x - 8))

Expand

2 (x^{2} + x + 1) + (2 x + 1) (2 x - 8) : 6 x^{2} - 12 x - 6

= 20 (6 x^{2} - 12 x - 6)

\frac{d}{d θ} (2 sin (θ))

\frac{d}{d x} (ln (12 - x))

\frac{d}{d x} (cos^{2} (ln (x^{3} + 3 x)))

\int tan^{5} (\frac{x}{2}) d x

\frac{d}{d x} (\frac{( x ^{7} )}{x ^{14} + 1})

What is the derivative of (2x-84(x^2+x+1)5) ?
The derivative of (2x-84(x^2+x+1)5) is 20(6x^2-12x-6)
What is the first derivative of (2x-84(x^2+x+1)5) ?
The first derivative of (2x-84(x^2+x+1)5) is 20(6x^2-12x-6)