A null derivative occurs when an increasing function does not have a derivative. This is most commonly seen in the question mark function.
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"Derivative of"
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.
The null set. Every set is a subset of itself and so the null set is a subset of the null set.
A null set is a set with nothing in it. A set containing a null set is still containing a "null set". Therefore it is right to say that the null set is not the same as a set containing only the null set.
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