What is the derivative of 1/3*(x-5^3) ?

The derivative of 1/3*(x-5^3) is (x-5)^2

What is the first derivative of 1/3*(x-5^3) ?

The first derivative of 1/3*(x-5^3) is (x-5)^2

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\frac{d}{d x} (\frac{1}{3} \cdot (x - 5)^{3})

(x - 5)^{2}

Solution steps

\frac{d}{d x} (\frac{1}{3} (x - 5)^{3})

Take the constant out:

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

= \frac{1}{3} \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

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

Simplify

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

= (x - 5)^{2}

What is the derivative of 1/3*(x-5^3) ?
The derivative of 1/3*(x-5^3) is (x-5)^2
What is the first derivative of 1/3*(x-5^3) ?
The first derivative of 1/3*(x-5^3) is (x-5)^2