What is the derivative of (x^2+18(2x+15)) ?

The derivative of (x^2+18(2x+15)) is 6x^2+30x+36

What is the first derivative of (x^2+18(2x+15)) ?

The first derivative of (x^2+18(2x+15)) is 6x^2+30x+36

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\frac{d}{d x} ((x^{2} + 18) (2 x + 15))

6 x^{2} + 30 x + 36

Solution steps

\frac{d}{d x} ((x^{2} + 18) (2 x + 15))

Apply the Product Rule:

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

f = x^{2} + 18, g = 2 x + 15

= \frac{d}{d x} (x^{2} + 18) (2 x + 15) + \frac{d}{d x} (2 x + 15) (x^{2} + 18)

\frac{d}{d x} (x^{2} + 18) = 2 x

\frac{d}{d x} (2 x + 15) = 2

= 2 x (2 x + 15) + 2 (x^{2} + 18)

Simplify

2 x (2 x + 15) + 2 (x^{2} + 18) : 6 x^{2} + 30 x + 36

= 6 x^{2} + 30 x + 36

What is the derivative of (x^2+18(2x+15)) ?
The derivative of (x^2+18(2x+15)) is 6x^2+30x+36
What is the first derivative of (x^2+18(2x+15)) ?
The first derivative of (x^2+18(2x+15)) is 6x^2+30x+36