How do you find the second derivative of #sin(x)/(1cos(x))#?
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You take the first derivative twice.
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To find the second derivative of sin(x)/(1cos(x)), follow these steps:
 Differentiate the function with respect to x to find the first derivative.
 Differentiate the first derivative obtained in step 1 with respect to x to find the second derivative.
Let's denote the function as y = sin(x)/(1cos(x)).

Find the first derivative (dy/dx) using the quotient rule: dy/dx = [(1cos(x))(cos(x))  sin(x)(sin(x))]/(1cos(x))^2

Simplify the expression: dy/dx = (cos(x)  cos^2(x)  sin^2(x))/(1cos(x))^2 dy/dx = (cos(x)  1)/(1cos(x))^2

Now, differentiate dy/dx with respect to x to find the second derivative: d^2y/dx^2 = d/dx[(cos(x)  1)/(1cos(x))^2]

Apply the quotient rule again: d^2y/dx^2 = [(1cos(x))^2(sin(x))  (cos(x)  1)(2(1cos(x))sin(x))]/(1cos(x))^4

Simplify the expression: d^2y/dx^2 = [(1cos(x))^2sin(x)  2(cos(x)  1)(1cos(x))sin(x)]/(1cos(x))^4 d^2y/dx^2 = [sin(x)(1cos(x))^2  2sin(x)(cos(x)  1)(1cos(x))]/(1cos(x))^4

Further simplify the expression: d^2y/dx^2 = [sin(x)(1cos(x))^2  2sin(x)(1cos(x))^2 + 2sin(x)(1cos(x))^3]/(1cos(x))^4 d^2y/dx^2 = [3sin(x)(1cos(x))^2 + 2sin(x)(1cos(x))^3]/(1cos(x))^4
Therefore, the second derivative of sin(x)/(1cos(x)) is: d^2y/dx^2 = [3sin(x)(1cos(x))^2 + 2sin(x)(1cos(x))^3]/(1cos(x))^4
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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