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The derivative of a function multiplied by a constant ($c$) is equal to the constant times the derivative of the function
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$c\frac{d}{dx}\left(x\ln\left(x\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of cxln(x). The derivative of a function multiplied by a constant (c) is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\ln\left(x\right). The derivative of the linear function is equal to 1. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}.