What is the derivative of f(x)=(x^3-2)^3 ?

The derivative of f(x)=(x^3-2)^3 is 9x^2(x^3-2)^2

What is the first derivative of f(x)=(x^3-2)^3 ?

The first derivative of f(x)=(x^3-2)^3 is 9x^2(x^3-2)^2

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derivative of

f (x) = (x^{3} - 2)^{3}

9 x^{2} (x^{3} - 2)^{2}

Solution steps

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

Apply the chain rule:

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

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

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

= 3 (x^{3} - 2)^{2} \cdot 3 x^{2}

Simplify

= 9 x^{2} (x^{3} - 2)^{2}

What is the derivative of f(x)=(x^3-2)^3 ?
The derivative of f(x)=(x^3-2)^3 is 9x^2(x^3-2)^2
What is the first derivative of f(x)=(x^3-2)^3 ?
The first derivative of f(x)=(x^3-2)^3 is 9x^2(x^3-2)^2