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Popular >

derivative of (2x-45(x^2+162))

Solution

\frac{d}{d x} ((2 x - 45) (x^{2} + 162))

Solution

6 x^{2} - 90 x + 324

Solution steps

\frac{d}{d x} ((2 x - 45) (x^{2} + 162))

Apply the Product Rule:

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

f = 2 x - 45, g = x^{2} + 162

= \frac{d}{d x} (2 x - 45) (x^{2} + 162) + \frac{d}{d x} (x^{2} + 162) (2 x - 45)

\frac{d}{d x} (2 x - 45) = 2

\frac{d}{d x} (x^{2} + 162) = 2 x

= 2 (x^{2} + 162) + 2 x (2 x - 45)

Simplify

2 (x^{2} + 162) + 2 x (2 x - 45) : 6 x^{2} - 90 x + 324

= 6 x^{2} - 90 x + 324

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Frequently Asked Questions (FAQ)

What is the derivative of (2x-45(x^2+162)) ?
The derivative of (2x-45(x^2+162)) is 6x^2-90x+324
What is the first derivative of (2x-45(x^2+162)) ?
The first derivative of (2x-45(x^2+162)) is 6x^2-90x+324