What Is the Derivative of 2e^x?

2ex is the derivative of 2ex, where two is a constant. With a derivative, any constant multiplied by a variable remains unchanged. ex is the derivative of x.

The exponential function is Ex. This function’s base is e, Euler’s number. This is an irrational number about equal to 2.71. The letter “e” ought to be considered as any other numerical base, such as two or three. If the exponential function has a numerical base “a,” it can be expressed as y = axe. This function’s derivative is dy/dx = (ax)ln (a). For instance, the derivative of the equation y=2x is dy/dx=(2x)ln (2). Consequently, the derivative of ex is (ex)ln (e). The natural log of e, denoted by ln(e), is 1. Therefore, the derivative reduces to ex.

If the function’s exponent contains anything more complex than an x, the chain rule must be applied. The derivative is determined in the same manner as previously, and then it is multiplied by the derivative of the exponent. For instance, if the exponent is 2x, its derivative is 2. The derivative is 2x if the exponent is x2. The derivative of the function y=2e(2x) is dy/dx=(2e2x)(2), which simplifies to dy/dx=4e (2x).

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