Solve p(x) =k x^k /k

Evaluate

p (x) = k \times \frac{x ^{k}}{k}

Simplify

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p (x) = x^{k}

Take the derivative of both sides

p^{'} (x) = \frac{d}{d x} (x^{k})

Rewrite the expression

p^{'} (x) = \frac{d}{d x} (e^{l n (x^{k})})

Calculate

p^{'} (x) = \frac{d}{d x} (e^{k l n (x)})

Use the chain rule \frac{d}{d x} (f (g)) = \frac{d}{d g} (f (g)) \times \frac{d}{d x} (g) where the g = k ln (x), to find the derivative

p^{'} (x) = \frac{d}{d g} (e^{g}) \times \frac{d}{d x} (k ln (x))

Use \frac{d}{d x} e^{x} = e^{x} to find derivative

p^{'} (x) = e^{g} \times \frac{d}{d x} (k ln (x))

Calculate

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p^{'} (x) = e^{g} \times \frac{k}{x}

Substitute back

p^{'} (x) = e^{k l n (x)} \times \frac{k}{x}

Calculate

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p^{'} (x) = x^{k} \times \frac{k}{x}

Solution

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p^{'} (x) = k x^{k - 1}

Function