What is the derivative of f(x)=(3x+1)(5x+4) ?

The derivative of f(x)=(3x+1)(5x+4) is 30x+17

What is the first derivative of f(x)=(3x+1)(5x+4) ?

The first derivative of f(x)=(3x+1)(5x+4) is 30x+17

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derivative of

f (x) = (3 x + 1) (5 x + 4)

30 x + 17

Solution steps

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

Apply the Product Rule:

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

f = 3 x + 1, g = 5 x + 4

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

\frac{d}{d x} (3 x + 1) = 3

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

= 3 (5 x + 4) + 5 (3 x + 1)

Simplify

3 (5 x + 4) + 5 (3 x + 1) : 30 x + 17

= 30 x + 17

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What is the derivative of f(x)=(3x+1)(5x+4) ?
The derivative of f(x)=(3x+1)(5x+4) is 30x+17
What is the first derivative of f(x)=(3x+1)(5x+4) ?
The first derivative of f(x)=(3x+1)(5x+4) is 30x+17