I am having trouble understanding the solution to a particular problem. The problem is this:
Differentiate f(x)=ln(sin(x)) - (x^4-3x)^10.
I can differentiate the second part of the function, but I dont quite understand differentiating the first part. I want to write (1/x)(sin(x))(cos(x)), but the solution says that it is cos(x)/(sinx(x).
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
To differentiate the first part, you must use the chain rule. \[d/dx[\ln(\sin(x))]=(1/\sin(x))*\cos(x)=cot(x)\]
Then, you just add the derivative of the first part to the derivative of the second part. :)
Ahh. I thought about that, but thought 1/sin(x) was wrong.
The reason why the derivative of ln(sin(x)) is cos(x)/sin(x) instead of (1/x)*(1/sin(x))*cos(x) is that when you differentiate the natural log, it turns into 1/(whatever what inside) not just 1/x times 1/(whatever was inside)