What is the derivative of (x-5^3) ?

The derivative of (x-5^3) is 3(x-5)^2

What is the first derivative of (x-5^3) ?

The first derivative of (x-5^3) is 3(x-5)^2

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\frac{d}{d x} ((x - 5)^{3})

3 (x - 5)^{2}

Solution steps

\frac{d}{d x} ((x - 5)^{3})

Apply the chain rule:

3 (x - 5)^{2} \frac{d}{d x} (x - 5)

= 3 (x - 5)^{2} \frac{d}{d x} (x - 5)

\frac{d}{d x} (x - 5) = 1

= 3 (x - 5)^{2} \cdot 1

Simplify

= 3 (x - 5)^{2}

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What is the derivative of (x-5^3) ?
The derivative of (x-5^3) is 3(x-5)^2
What is the first derivative of (x-5^3) ?
The first derivative of (x-5^3) is 3(x-5)^2