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The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
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$\frac{1}{2}\left(5x\right)^{-\frac{1}{2}}\frac{d}{dx}\left(5x\right)$
Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx((5x)^1/2). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The derivative of the constant function (5) is equal to zero. Any expression multiplied by 0 is equal to 0.