(1+cosx)/sinx derivative | What is derivative of (1+cosx)/(sinx)?

Greetings everyone. In this article, we will tell you what is the derivative of the expression (1+cosx)/sinx. We wish everyone good lessons and good work in advance.

What is derivative of (1+cosx)/(sinx)?

1+cosx/sinx derivative

👉 First, let's write our question.

= $\frac{d}{dx}(\frac{1+cosx}{sinx})$

👉 Here, we divide the numerator and denominator into 2 in order to take derivatives easily. So our new question goes like this;

= $\frac{d}{dx}({\frac{1}{sinx}+\frac{cosx}{sinx}})$

👉 So, first we will take the derivative of 1/sinx, then we will take the derivative of cosx/sinx, that is, cotx. Let's write step by step;

we can transform = $\frac{1}{sinx}=cosecx=cscx$

we can transform = $\frac{cosx}{sinx}=cotx$

👉 So, lets continue;

= $\frac{d}{dx}(cosecx+cotx)$

= ${-cotx.cosecx}-cosec^2x$

Our answer = ${-cotx.cosecx}-{cosecx}^2$

Thank you and good lesson.