$\frac{d}{dx}\left(x\sqrt{x^2-1}\right)$
$\frac{d}{dx}\left(\sqrt{x}ln\left(x\right)\right)$
$\frac{d}{dx}\left(\sqrt{\frac{x\left(x+2\right)}{\left(2x+1\right)\left(5x+3\right)}}\right)$
$\frac{d}{dx}x\ln\left(x\right)$
$\frac{d}{dx}\left(xe^{2x}\right)$
$\frac{d}{dx}\left(x\sqrt{x^2+1}\right)$
$\frac{d}{dx}\left(\cos\left(x\right)\right)\cdot \csc\left(x\right)$
The product rule is a formula used to find the derivatives of products of two or more functions. It may be stated as $(f\cdot g)'=f'\cdot g+f\cdot g'$
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