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Popular >

derivative of (2x+5)(5x^2+1)

Solution

derivative of

(2 x + 5) (5 x^{2} + 1)

Solution

30 x^{2} + 50 x + 2

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (5 x^{2} + 1) = 10 x

= 2 (5 x^{2} + 1) + 10 x (2 x + 5)

Simplify

2 (5 x^{2} + 1) + 10 x (2 x + 5) : 30 x^{2} + 50 x + 2

= 30 x^{2} + 50 x + 2

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Frequently Asked Questions (FAQ)

What is the derivative of (2x+5)(5x^2+1) ?
The derivative of (2x+5)(5x^2+1) is 30x^2+50x+2
What is the first derivative of (2x+5)(5x^2+1) ?
The first derivative of (2x+5)(5x^2+1) is 30x^2+50x+2