What is the derivative of 2x(6x-18^6) ?

The derivative of 2x(6x-18^6) is 2((6x-18)^6+36x(6x-18)^5)

What is the first derivative of 2x(6x-18^6) ?

The first derivative of 2x(6x-18^6) is 2((6x-18)^6+36x(6x-18)^5)

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\frac{d}{d x} (2 x (6 x - 18)^{6})

2 ((6 x - 18)^{6} + 36 x (6 x - 18)^{5})

Solution steps

\frac{d}{d x} (2 x (6 x - 18)^{6})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (x (6 x - 18)^{6})

Apply the Product Rule:

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

f = x, g = (6 x - 18)^{6}

= 2 (\frac{d x}{d x} (6 x - 18)^{6} + \frac{d}{d x} ((6 x - 18)^{6}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} ((6 x - 18)^{6}) = 36 (6 x - 18)^{5}

= 2 (1 \cdot (6 x - 18)^{6} + 36 (6 x - 18)^{5} x)

Simplify

= 2 ((6 x - 18)^{6} + 36 x (6 x - 18)^{5})

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What is the derivative of 2x(6x-18^6) ?
The derivative of 2x(6x-18^6) is 2((6x-18)^6+36x(6x-18)^5)
What is the first derivative of 2x(6x-18^6) ?
The first derivative of 2x(6x-18^6) is 2((6x-18)^6+36x(6x-18)^5)