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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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$\frac{1}{s\left(\csc\left(x\right)+\cot\left(x\right)\right)}\frac{d}{ds}\left(s\left(\csc\left(x\right)+\cot\left(x\right)\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of ln(s(csc(x)+cot(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}. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=s and g=\csc\left(x\right)+\cot\left(x\right). The derivative of the linear function is equal to 1. The derivative of a sum of two or more functions is the sum of the derivatives of each function.