Derivatives are used to find instantaneous rate at which a function changes.
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Because it is calculated as the limiting value of the change divided by the time taken for the change, the limit being taken as the time interval becomes infinitesimally small. That is how the derivative with respect to time is defined.
"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.
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
The derivative of xe is e. The derivative of xe is exe-1.