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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
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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
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.
How do you find second derivative of a function?
All it means to take the second derivative is to take the derivative of a function twice. For example, say you start with the function y=x2+2x The first derivative would be 2x+2 But when you take the derivative the first derivative you get the second derivative which would be 2
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.
What is the derivative of x to the second powerr?
2x is the first derivative of x2.
What is the derivative of x to the second power?
2x is the first derivative of x2.
Does The second derivative represent the rate of change of the first derivative?
Yes.
How do you find the second derivative?
Afetr you take the first derivative you take it again Example y = x^2 dy/dx = 2x ( first derivative) d2y/dx2 = 2 ( second derivative)
How do you get the second derivative of potential energy?
To get the second derivative of potential energy, you first need to calculate the first derivative of potential energy with respect to the variable of interest. Then, you calculate the derivative of this expression. This second derivative gives you the rate of change of the slope of the potential energy curve, providing insight into the curvature of the potential energy surface.
What is the derivative value at an inflection point?
the second derivative at an inflectiion point is zero
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
What is the second derivative of x to the fourth power?
d/dx(X^4) = 4X^3 ( first derivative ) d/dx(4X^3) = 12X^2 ( second derivative )
