Two is a constant, hence 2ex is the derivative of 2e. When taking a derivative, any constant multiplied by a variable stays the same. EX is the derivative of EX.
E^x is an exponential function. The Euler’s number, e, serves as the function’s base. This value is roughly 2.71 and is unreasonable. E should be regarded like any other numerical base, such as 2 or 3, in terms of treatment.
The exponential function can be expressed as y = axe if its numerical base is “a”. This function’s derivative is dy/dx = (ax)ln (a). For instance, dy/dx=(2x)ln is the derivative of the equation y=2x (2). Thus the derivative of e^x is (e^x)ln(e) (e). Ln(e), the natural log of e, is one. As a result, the derivative becomes ex.
Use of the chain rule is required if the function has anything in the exponent other than an x. The derivative is calculated identically as previously, and it is then multiplied by the exponent’s derivative.
For instance, the derivative of 2x is two if the exponent is 2x. The derivative is 2x if the exponent is x2. The derivative for the function y=2e(2x) is dy/dx=(2e(2x))(2), which is equivalent to dy/dx=4e (2x).