The derivative of csc x is…
To find the derivative of csc x, we can use the quotient rule
To find the derivative of csc x, we can use the quotient rule. The quotient rule states that for two functions u(x) and v(x), the derivative of their quotient, u(x) / v(x), is given by the formula:
d/dx (u(x) / v(x)) = [v(x)*u'(x) – u(x)*v'(x)] / [v(x)]^2
In this case, u(x) represents the function 1, and v(x) represents the function sin x. Therefore, we have:
u(x) = 1
v(x) = sin x
Differentiating u(x) and v(x) with respect to x, we have:
u'(x) = 0 (since the derivative of a constant is zero)
v'(x) = cos x (since the derivative of sin x is cos x)
Applying the quotient rule, we get:
d/dx (csc x) = [sin x * 0 – 1 * cos x] / [sin x]^2
= -cos x / sin^2 x
Therefore, the derivative of csc x is equal to -cos x / sin^2 x.
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