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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 differential calculus problems step by step online. Find the derivative using the quotient 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}. The derivative of the linear function times a constant, is equal to the constant. The derivative of the linear function is equal to 1. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number.