Looks like simple difference formula work here.
f(x) - g(x)
= f'(x) - g'(x)
e - 5x
= e - 5
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You can use the L'hopital's rule to calculate the limit of e5x -1 divided by sin x as x approaches 0.
"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.