What is the derivative of g(x)=3(4-9x)^4 ?

The derivative of g(x)=3(4-9x)^4 is -108(4-9x)^3

What is the first derivative of g(x)=3(4-9x)^4 ?

The first derivative of g(x)=3(4-9x)^4 is -108(4-9x)^3

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derivative of

g (x) = 3 (4 - 9 x)^{4}

- 108 (4 - 9 x)^{3}

Solution steps

\frac{d}{d x} (3 (4 - 9 x)^{4})

Take the constant out:

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

= 3 \frac{d}{d x} ((4 - 9 x)^{4})

Apply the chain rule:

4 (4 - 9 x)^{3} \frac{d}{d x} (4 - 9 x)

= 4 (4 - 9 x)^{3} \frac{d}{d x} (4 - 9 x)

\frac{d}{d x} (4 - 9 x) = - 9

= 3 \cdot 4 (4 - 9 x)^{3} (- 9)

Simplify

= - 108 (4 - 9 x)^{3}

What is the derivative of g(x)=3(4-9x)^4 ?
The derivative of g(x)=3(4-9x)^4 is -108(4-9x)^3
What is the first derivative of g(x)=3(4-9x)^4 ?
The first derivative of g(x)=3(4-9x)^4 is -108(4-9x)^3