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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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$\frac{1}{2}\left(1-\cos\left(x\right)\right)^{-\frac{1}{2}}\frac{d}{dx}\left(1-\cos\left(x\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of d/dx((1-cos(x))^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 a sum of two or more functions is the sum of the derivatives of each function. The derivative of the constant function (1) is equal to zero. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.