d/dx (cotx)=
(-cscx)∧2
To differentiate cot(x) with respect to x, we can rewrite the expression as cos(x)/sin(x).
Using the quotient rule of differentiation,
d/dx [cos(x)/sin(x)] = (sin(x)(-sin(x)) – cos(x)cos(x)) / [sin(x)sin(x)]
= (-sin^2(x) – cos^2(x)) / [sin^2(x)]
Using the trigonometric identity sin^2(x) + cos^2(x) = 1, we get
d/dx [cos(x)/sin(x)] = -1/sin^2(x)
Therefore, the derivative of cot(x) with respect to x is -csc^2(x).
In short,
d/dx (cotx) = -csc^2(x)
More Answers:
[next_post_link]