What is the derivative of (2x-7)4(x^2+x+1)5 ?

The derivative of (2x-7)4(x^2+x+1)5 is 20(6x^2-10x-5)

What is the first derivative of (2x-7)4(x^2+x+1)5 ?

The first derivative of (2x-7)4(x^2+x+1)5 is 20(6x^2-10x-5)

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derivative of

(2 x - 7) 4 (x^{2} + x + 1) 5

20 (6 x^{2} - 10 x - 5)

Solution steps

\frac{d}{d x} ((2 x - 7) \cdot 4 (x^{2} + x + 1) \cdot 5)

Simplify

(2 x - 7) \cdot 4 (x^{2} + x + 1) \cdot 5 : 20 (2 x - 7) (x^{2} + x + 1)

= \frac{d}{d x} (20 (2 x - 7) (x^{2} + x + 1))

Take the constant out:

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

= 20 \frac{d}{d x} ((2 x - 7) (x^{2} + x + 1))

Apply the Product Rule:

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

f = 2 x - 7, g = x^{2} + x + 1

= 20 (\frac{d}{d x} (2 x - 7) (x^{2} + x + 1) + \frac{d}{d x} (x^{2} + x + 1) (2 x - 7))

\frac{d}{d x} (2 x - 7) = 2

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

= 20 (2 (x^{2} + x + 1) + (2 x + 1) (2 x - 7))

Expand

2 (x^{2} + x + 1) + (2 x + 1) (2 x - 7) : 6 x^{2} - 10 x - 5

= 20 (6 x^{2} - 10 x - 5)

What is the derivative of (2x-7)4(x^2+x+1)5 ?
The derivative of (2x-7)4(x^2+x+1)5 is 20(6x^2-10x-5)
What is the first derivative of (2x-7)4(x^2+x+1)5 ?
The first derivative of (2x-7)4(x^2+x+1)5 is 20(6x^2-10x-5)