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Learn how to solve problems step by step online. Find the derivative of ln(((x^4-5)^2)/(cos(x)^6(x^4-5)^6)). Simplifying. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. 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}. Multiplying the fraction by -1.
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