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Popular >

derivative of (2x+5(3x^2-4x+1))

Solution

\frac{d}{d x} ((2 x + 5) (3 x^{2} - 4 x + 1))

Solution

18 x^{2} + 14 x - 18

Solution steps

\frac{d}{d x} ((2 x + 5) (3 x^{2} - 4 x + 1))

Apply the Product Rule:

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

f = 2 x + 5, g = 3 x^{2} - 4 x + 1

= \frac{d}{d x} (2 x + 5) (3 x^{2} - 4 x + 1) + \frac{d}{d x} (3 x^{2} - 4 x + 1) (2 x + 5)

\frac{d}{d x} (2 x + 5) = 2

\frac{d}{d x} (3 x^{2} - 4 x + 1) = 6 x - 4

= 2 (3 x^{2} - 4 x + 1) + (6 x - 4) (2 x + 5)

Simplify

2 (3 x^{2} - 4 x + 1) + (6 x - 4) (2 x + 5) : 18 x^{2} + 14 x - 18

= 18 x^{2} + 14 x - 18

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Frequently Asked Questions (FAQ)

What is the derivative of (2x+5(3x^2-4x+1)) ?
The derivative of (2x+5(3x^2-4x+1)) is 18x^2+14x-18
What is the first derivative of (2x+5(3x^2-4x+1)) ?
The first derivative of (2x+5(3x^2-4x+1)) is 18x^2+14x-18