What is the derivative of (2x+3(x^2-5)) ?

The derivative of (2x+3(x^2-5)) is 6x^2+6x-10

What is the first derivative of (2x+3(x^2-5)) ?

The first derivative of (2x+3(x^2-5)) is 6x^2+6x-10

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

6 x^{2} + 6 x - 10

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 (x^{2} - 5) + 2 x (2 x + 3) : 6 x^{2} + 6 x - 10

= 6 x^{2} + 6 x - 10

What is the derivative of (2x+3(x^2-5)) ?
The derivative of (2x+3(x^2-5)) is 6x^2+6x-10
What is the first derivative of (2x+3(x^2-5)) ?
The first derivative of (2x+3(x^2-5)) is 6x^2+6x-10