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Trig functions have their own special derivatives that you will have to memorize.

For instance:

the derivative of sinx is cosx.

The derivative of cosx is -sinx

The derivative of tanx is sec2x

The derivative of cscx is -cscxcotx

The derivative of secx is secxtanx

The derivative of cotx is -csc2x

Q: How do you take the derivative of a trig function?

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Yes, sine is a trig function, it is opposite over hypotenuse.

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.

A null derivative occurs when an increasing function does not have a derivative. This is most commonly seen in the question mark function.

A linear function, for example y(x) = ax + b has the first derivative a.

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.

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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

The same way you get the second derivative from any function. Assuming you have a function that expresses potential energy as a function of time, or perhaps as a function of position, you take the derivate of this function. This will give you another function. Then, you take the derivate of this derivative, to get the second derivative.

Yes, sine is a trig function, it is opposite over hypotenuse.

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.

Take the derivative of the function.

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All six trigonometric functions can take the value 1.

The only trig functions i can think of with horizontal assymptotes are the inverse trig functions. and they go assymptotic for everytime the non-inverse function is equal to zero.

You take the derivative using only one variable. The other variables act as constants.

A null derivative occurs when an increasing function does not have a derivative. This is most commonly seen in the question mark function.

You can differentiate a function when it only contains one changing variable, like f(x) = x2. It's derivative is f'(x) = 2x. If a function contains more than one variable, like f(x,y) = x2 + y2, you can't just "find the derivative" generically because that doesn't specify what variable to take the derivative with respect to. Instead, you might "take the derivative with respect to x (treating y as a constant)" and get fx(x,y) = 2x or "take the derivative with respect to y (treating x as a constant)" and get fy(x,y) = 2y. This is a partial derivative--when you take the derivative of a function with many variable with respect to one of the variables while treating the rest as constants.

A linear function, for example y(x) = ax + b has the first derivative a.