What is the derivative of f(x)=(2x^3+6x)(4x^2-7x+11) ?

The derivative of f(x)=(2x^3+6x)(4x^2-7x+11) is 40x^4-56x^3+138x^2-84x+66

What is the first derivative of f(x)=(2x^3+6x)(4x^2-7x+11) ?

The first derivative of f(x)=(2x^3+6x)(4x^2-7x+11) is 40x^4-56x^3+138x^2-84x+66

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derivative of

f (x) = (2 x^{3} + 6 x) (4 x^{2} - 7 x + 11)

40 x^{4} - 56 x^{3} + 138 x^{2} - 84 x + 66

Solution steps

\frac{d}{d x} ((2 x^{3} + 6 x) (4 x^{2} - 7 x + 11))

Apply the Product Rule:

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

f = 2 x^{3} + 6 x, g = 4 x^{2} - 7 x + 11

= \frac{d}{d x} (2 x^{3} + 6 x) (4 x^{2} - 7 x + 11) + \frac{d}{d x} (4 x^{2} - 7 x + 11) (2 x^{3} + 6 x)

\frac{d}{d x} (2 x^{3} + 6 x) = 6 x^{2} + 6

\frac{d}{d x} (4 x^{2} - 7 x + 11) = 8 x - 7

= (6 x^{2} + 6) (4 x^{2} - 7 x + 11) + (8 x - 7) (2 x^{3} + 6 x)

Simplify

(6 x^{2} + 6) (4 x^{2} - 7 x + 11) + (8 x - 7) (2 x^{3} + 6 x) : 40 x^{4} - 56 x^{3} + 138 x^{2} - 84 x + 66

= 40 x^{4} - 56 x^{3} + 138 x^{2} - 84 x + 66

What is the derivative of f(x)=(2x^3+6x)(4x^2-7x+11) ?
The derivative of f(x)=(2x^3+6x)(4x^2-7x+11) is 40x^4-56x^3+138x^2-84x+66
What is the first derivative of f(x)=(2x^3+6x)(4x^2-7x+11) ?
The first derivative of f(x)=(2x^3+6x)(4x^2-7x+11) is 40x^4-56x^3+138x^2-84x+66