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Popular >

derivative of (2x^2+3(5x+3))

Solution

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

Solution

30 x^{2} + 12 x + 15

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (2 x^{2} + 3) = 4 x

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

= 4 x (5 x + 3) + 5 (2 x^{2} + 3)

Simplify

4 x (5 x + 3) + 5 (2 x^{2} + 3) : 30 x^{2} + 12 x + 15

= 30 x^{2} + 12 x + 15

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Frequently Asked Questions (FAQ)

What is the derivative of (2x^2+3(5x+3)) ?
The derivative of (2x^2+3(5x+3)) is 30x^2+12x+15
What is the first derivative of (2x^2+3(5x+3)) ?
The first derivative of (2x^2+3(5x+3)) is 30x^2+12x+15