It might become easier if you split the problem in half. Since we know that d/dx[f(x)-g(x)] is the same as the derivative of d/dx[f(x)] - d/dx[g(x)], you can rewrite your problem as d/dx(e)- d/dx(2x). (it's common usage to write coefficients in from of variables, but that's just notation). The derivative of e is simply 0 (since e is a constant) and the derivative of 2x is 2.
so d/dx(e-2x)=0-2=-2
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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.
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 40 is zero. The derivative of any constant is zero.
The derivative of xe is e. The derivative of xe is exe-1.