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Subjects>Math>Math & Arithmetic

What is the second derivative of ln(tan(x))?

Anonymous

∙ 9y ago

Updated: 10/25/2022

f'(x) = 1/tan(x) * sec^2(x) where * means multiply and ^ means to the power of.

= cot(x) * sec^2(x)

f''(x) = f'(cot(x)*sec^2(x) + cot(x)*f'[sec^2(x)]

= -csc^2(x)*sec^2(x) + cot(x)*2tan(x)sec^2(x)

= sec^2(x) [cot(x)-csc^2(x)] +2tan(x)cot(x)

= sec^2(x) [cot(x)-csc^2(x)] +2

Wiki User

∙ 9y ago

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What is the geometrical meaning for second derivative?

The Geometrical meaning of the second derivative is the curvature of the function. If the function has zero second derivative it is straight or flat.

What is the geometrical meaning of second derivative?

The first derivative is the rate of change, and the second derivative is the rate of change of the rate of change.

What is the second derivative of a function's indefinite integral?

well, the second derivative is the derivative of the first derivative. so, the 2nd derivative of a function's indefinite integral is the derivative of the derivative of the function's indefinite integral. the derivative of a function's indefinite integral is the function, so the 2nd derivative of a function's indefinite integral is the derivative of the function.

Does The second derivative represent the rate of change of the first derivative?

Yes.

If the 2nd derivative of an equation isn't constant is it still a quadratic relation?

No. A quadratic equation always has a second derivative that is a constant. For example -3x2 + 10x - 2 first derivative -6x + 10 second derivative -6

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