What is the derivative of (3x-4(5x+2)) ?

The derivative of (3x-4(5x+2)) is 30x-14

What is the first derivative of (3x-4(5x+2)) ?

The first derivative of (3x-4(5x+2)) is 30x-14

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

30 x - 14

Solution steps

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

Apply the Product Rule:

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

f = 3 x - 4, g = 5 x + 2

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

\frac{d}{d x} (3 x - 4) = 3

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

= 3 (5 x + 2) + 5 (3 x - 4)

Simplify

3 (5 x + 2) + 5 (3 x - 4) : 30 x - 14

= 30 x - 14

What is the derivative of (3x-4(5x+2)) ?
The derivative of (3x-4(5x+2)) is 30x-14
What is the first derivative of (3x-4(5x+2)) ?
The first derivative of (3x-4(5x+2)) is 30x-14