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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=
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$\frac{d}{dx}\left(x\right)\tan\left(xy\right)+x\frac{d}{dx}\left(\tan\left(xy\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of xtan(xy). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The derivative of the linear function is equal to 1. The derivative of the tangent of a function is equal to secant squared of that function times the derivative of that function, in other words, if {f(x) = tan(x)}, then {f'(x) = sec^2(x)\cdot D_x(x)}. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.