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 |

ðŸ‘‰ First, let's write our question.

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

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

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

ðŸ‘‰ 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

**= $\frac{cosx}{sinx}=cotx$**

ðŸ‘‰ So, lets continue;

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

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

Our answer =

**${-cotx.cosecx}-{cosecx}^2$**Thank you and good lesson.

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