In general, an exponential function is of the form
f(x) = ax where a is a positive constant.
Derivative of the Natural Exponential Function
The exponential function f(x) = ex has the property that it is its own derivative. This means that the slope of a tangent line to the curve y = ex at any point is equal to the y-coordinate of the point.
We can combine the above formula with the chain rule to get
Differentiate the function y = e sin x
Differentiate the function y = e–3xsin4x
Using the Product Rule and the above formulas, we get
Derivative of ax
Derivative of ag(x)
Differentiate y = x3 + 3x
Differentiate y = 52x+1
Derivatives of Exponential Functions
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