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Popular >

derivative of 10(3x+1(1-5x))

Solution

\frac{d}{d x} (10 (3 x + 1) (1 - 5 x))

Solution

10 (- 30 x - 2)

Solution steps

\frac{d}{d x} (10 (3 x + 1) (1 - 5 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 10 \frac{d}{d x} ((3 x + 1) (1 - 5 x))

Apply the Product Rule:

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

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

= 10 (\frac{d}{d x} (3 x + 1) (1 - 5 x) + \frac{d}{d x} (1 - 5 x) (3 x + 1))

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

\frac{d}{d x} (1 - 5 x) = - 5

= 10 (3 (1 - 5 x) + (- 5) (3 x + 1))

Simplify

10 (3 (1 - 5 x) + (- 5) (3 x + 1)) : 10 (- 30 x - 2)

= 10 (- 30 x - 2)

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Frequently Asked Questions (FAQ)

What is the derivative of 10(3x+1(1-5x)) ?
The derivative of 10(3x+1(1-5x)) is 10(-30x-2)
What is the first derivative of 10(3x+1(1-5x)) ?
The first derivative of 10(3x+1(1-5x)) is 10(-30x-2)