And I like to write it that way because I always forget the whole quotient rule thing.
#Derivative of log function examples plus
So that's going to be times and I'm going to rewrite it as the derivative with respect to X of X plus five times X minus one to the negative one power. And then it's going to be times, and I'll do this in magenta. So let's see, this is going to be equal to, let's use some colors here, this, what I'm boxing off in blue, that's the same thing as X minus one over X plus five. The derivative of this whole thing with respect to this expression, times the derivative of this expression with respect to X.
In that case, F prime of X is going to be the derivative of this whole thing with respect to X plus five over X minus one which is going to be one over X plus five over X minus one times the derivative, times the derivative with respect to X of X plus five over X minus one. 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. 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.
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