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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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$-\frac{1}{2}\left(9-x^2\right)^{-\frac{3}{2}}\frac{d}{dx}\left(9-x^2\right)$
Learn how to solve problems step by step online. Find the derivative using the product rule d/dx((9-x^2)^(-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. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=-1 and g=x^2. The derivative of the constant function (9) is equal to zero.