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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 $\displaystyle f'(x)=\frac{a'}{a}$
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$\frac{1}{5\cos\left(3x\sin\left(23x\right)\right)}\frac{d}{dx}\left(5\cos\left(3x\sin\left(23x\right)\right)\right)$
Learn how to solve problems step by step online. Find the derivative of ln(5cos(3xsin(23x))). 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}. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. 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 a function multiplied by a constant is equal to the constant times the derivative of the function.