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You can find this derivative by applying the Chain Rule, with cosx as the inner function, and lnx as the outer function. Process: To apply the chain rule, we first find the derivative of the outer function, lnu, with u = cosx. Remember that the derivative of lnu = 1/u = 1/cosx. Now we just need to find the derivative of the inner function, cosx, and multiply it by the derivative of the outer ...


The derivative of the natural log is 1/x, therefore the derivative is 1/cos(x). However, since the value of cos(x) is submitted within the natural log we must use the chain rule.


It seems to turn out to be -sin(x)/cos(x). As the derivative of ln(x) is 1/x and using the chain rule we multiply by the derivative of the inner which leaves us with -sin(x)/cos(x)?? Is this correct? If not please enlighten me..with a short proof. :-) thanks yall


Free derivative calculator - differentiate functions with all the steps. Type in any function derivative to get the solution, steps and graph


Calculus Examples. Popular Problems. Calculus. Find the Derivative - d/dx cos( natural log of x) Differentiate using the chain rule, which states that is where and . Tap for more steps... To apply the Chain Rule, set as . The derivative of with respect to is . Replace all occurrences of with .


The derivative of cos x is −sin x (note the negative sign!) and The derivative of tan x is sec 2 x . Now, if u = f ( x ) is a function of x , then by using the chain rule, we have:


Derivative of y = ln u (where u is a function of x). Unfortunately, we can only use the logarithm laws to help us in a limited number of logarithm differentiation question types. Most often, we need to find the derivative of a logarithm of some function of x.For example, we may need to find the derivative of y = 2 ln (3x 2 − 1).. We need the following formula to solve such problems.


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Learn how to find the derivative of ln(f(x)) The general formula for the derivative of ln(f(x)) the natural log of a general function is f'(x)/f(x)


The derivative of ln(x) is a well-known derivative. This lesson will show us the steps involved in finding this derivative, and it will go over a...