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The derivative of a function multiplied by a constant ($-1$) is equal to the constant times the derivative of the function
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$-\frac{d}{dx}\left(\cos\left(x\right)\ln\left(x\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of -cos(x)ln(x). The derivative of a function multiplied by a constant (-1) 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=\cos\left(x\right) and g=\ln\left(x\right). The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). 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}.