Dx {csc (x)}=?
To find the derivative of csc(x), we can use the chain rule
To find the derivative of csc(x), we can use the chain rule. Let’s break it down step by step:
The function csc(x) can be written as 1/sin(x). Now, let’s proceed with the differentiation using the quotient rule.
Step 1: Identify the numerator and denominator of our quotient function.
Numerator: 1
Denominator: sin(x)
Step 2: Apply the quotient rule, which states that if we have a function f(x) = g(x)/h(x), its derivative is given by (h(x)f'(x) – g(x)h'(x))/(h(x))^2.
Applying the quotient rule to our function, we have:
d/dx(csc(x)) = (sin(x)(0) – 1(cos(x)))/(sin(x))^2
Simplifying this expression gives us:
d/dx(csc(x)) = -cos(x)/(sin(x))^2
Therefore, the derivative of csc(x) is equal to -cos(x)/(sin(x))^2.
It’s important to remember that the domain of csc(x) excludes the values where sin(x) equals zero, as dividing by zero is undefined.
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