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Popular >

derivative of (x^3+7x-1(5x+2))

Solution

\frac{d}{d x} ((x^{3} + 7 x - 1) (5 x + 2))

Solution

20 x^{3} + 6 x^{2} + 70 x + 9

Solution steps

\frac{d}{d x} ((x^{3} + 7 x - 1) (5 x + 2))

Apply the Product Rule:

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

f = x^{3} + 7 x - 1, g = 5 x + 2

= \frac{d}{d x} (x^{3} + 7 x - 1) (5 x + 2) + \frac{d}{d x} (5 x + 2) (x^{3} + 7 x - 1)

\frac{d}{d x} (x^{3} + 7 x - 1) = 3 x^{2} + 7

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

= (3 x^{2} + 7) (5 x + 2) + 5 (x^{3} + 7 x - 1)

Simplify

(3 x^{2} + 7) (5 x + 2) + 5 (x^{3} + 7 x - 1) : 20 x^{3} + 6 x^{2} + 70 x + 9

= 20 x^{3} + 6 x^{2} + 70 x + 9

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Frequently Asked Questions (FAQ)

What is the derivative of (x^3+7x-1(5x+2)) ?
The derivative of (x^3+7x-1(5x+2)) is 20x^3+6x^2+70x+9
What is the first derivative of (x^3+7x-1(5x+2)) ?
The first derivative of (x^3+7x-1(5x+2)) is 20x^3+6x^2+70x+9