I had actually a Calculus 1 test on inverse attributes today and also one of the concerns asked "What is the antiderivative that \$ an\$?".

You are watching: Derivative of ln(cosx)

I know now the the appropriate answer is \$ln(sec x) + C\$, however the prize I placed was \$ln|-cos x| + C\$ and I to be wondering if the answer would additionally work. My logic is the the derivative of my answer would be \$dfrac 1 cos x sin x\$ which would certainly simplify come \$ an x\$.

Can someone simply tell me if mine answer to be right, and if it was wrong what would the derivative of my answer in reality be.

The derivative that \$f(x)=ln|x|\$ is \$f"(x)=frac1x\$. For this reason the derivative that \$ln|-cos x|\$ is \$fracsin x-cos x\$. This is because the derivative the \$-cos x\$ is \$sin x\$.

So the derivative of your expression is \$- an x\$.

\$\$y=ln|-cos x|=lnsqrt(-cos x)^2=frac12ln(-cos x)^2=frac12ln(cos^2 x)\$\$\$\$y"=frac12(frac-2cos x sin xcos^2 x)=- an x\$\$

We have\$\$ fracddx log(kcosx) = frac-ksinxkcosx \$\$by applying the chain rule. Everything the value of \$k\$, the derivative is \$- anx\$.

Thanks because that contributing response to hunterriverpei.comematics Stack Exchange!

Please be certain to answer the question. Carry out details and also share her research!

But avoid

Asking for help, clarification, or responding to various other answers.Making statements based on opinion; ago them increase with recommendations or an individual experience.

Use hunterriverpei.comJax to format equations. hunterriverpei.comJax reference.

See more: How Many Cc In A Ml Syringe ? How Much Is A Cc On An Ml Syringe

To discover more, view our tips on writing an excellent answers.