Simplify this expression using this property and just to try and power through this using the chain rule. Now what's the hard way you might be thinking? Or maybe you did do it when you tried to approach it on your own. And the derivative of this, well, let's see, we're going to have a minus sign there and the derivative of the natural log of X minus one with respect to X minus one is going to be one over X minus one and the derivative of X minus one with the respect to X is just one you just multiply this by one, it doesn't really change the value. I'm just applying the chain rule here, and that's just going to be one. And when we take the derivative now with respect to X, F prime of X, well this is going to be the derivative of the natural log of X plus five with respect to X plus five, so that's going to be one over X plus five times the derivative of X plus five with respect to X.
We can write F of X as being equal to the natural log of X plus five minus the natural log of X minus one. It from a point of view in terms of having to
So if we just apply this property right over here, and just simplify this expression, or at least simplify So this is just going to be equal to the natural log of A minus the natural log of B. The easy way is to recognize your logarithm properties, to remember that the natural log of A over B. And I encourage you to pause this video and try to figure it out on your own. And what we want to figure out is what is F prime of X.
So, we have, $\dfrac$.Voiceover:Let's say that we've got the function F of X and it is equal to the natural log of X plus five over X minus one. Also derivatives of 2x with respect to x must be remembered in order to solve the given problem. So, differentiation of $\log 2x$ with respect to x will be done layer by layer using the chain rule of differentiation. Since, $\log 2x$ is a composite function, we will have to apply the chain rule of differentiation in the process of differentiating $\log 2x$. Hint: In the given problem, we are required to differentiate $\log 2x$ with respect to x.
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