The derivative of sin (x) is cos (x). It does not work the other way around, though. The derivative of cos (x) is -sin (x).
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y = Sin(pi) = 0 Then its derivative is dy/dx = Cos(pi). = -1
The derivative of ex is ex. The derivative of ex is e.
The derivative of ex is ex
d/dx (ex + x3) = ex + 3x2
The derivative of x is not x. X is the same as x^1, so you use the power rule which decreases the power by one and brings the exponent down, giving 1x^0, which is equal to 1.