What is the derivative of f(x)=(2+3x)(6-5x) ?

The derivative of f(x)=(2+3x)(6-5x) is -30x+8

What is the first derivative of f(x)=(2+3x)(6-5x) ?

The first derivative of f(x)=(2+3x)(6-5x) is -30x+8

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derivative of

f (x) = (2 + 3 x) (6 - 5 x)

- 30 x + 8

Solution steps

\frac{d}{d x} ((2 + 3 x) (6 - 5 x))

Apply the Product Rule:

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

f = 2 + 3 x, g = 6 - 5 x

= \frac{d}{d x} (2 + 3 x) (6 - 5 x) + \frac{d}{d x} (6 - 5 x) (2 + 3 x)

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

\frac{d}{d x} (6 - 5 x) = - 5

= 3 (6 - 5 x) + (- 5) (2 + 3 x)

Simplify

3 (6 - 5 x) + (- 5) (2 + 3 x) : - 30 x + 8

= - 30 x + 8

What is the derivative of f(x)=(2+3x)(6-5x) ?
The derivative of f(x)=(2+3x)(6-5x) is -30x+8
What is the first derivative of f(x)=(2+3x)(6-5x) ?
The first derivative of f(x)=(2+3x)(6-5x) is -30x+8