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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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$\frac{1}{2}\left(x+y\right)^{-\frac{1}{2}}\frac{d}{dx}\left(x+y\right)=xy$
Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative d/dx((x+y)^1/2)=xy. 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 a sum of two or more functions is the sum of the derivatives of each function. The derivative of the linear function is equal to 1. The derivative of the linear function is equal to 1.