d dxex=ex d dxef(x)=f (x)ef(x) Differentiate the exponent and multiply by the original exponential function. Example Differentiate e7x2+1 with respect to x. ddxe7x2+1 =e7x2+1(14x) =14xe7x2+1

\(\dfrac{\mathrm d}{\mathrm dx}e^x=e^x\qquad\dfrac{\mathrm d}{\mathrm dx}e^{f(x)}=\mathrm{f}^{\prime}(x)e^{f(x)}\)

Differentiate the exponent and multiply by the original exponential function.

Differentiate \(e^{7x^2+1}\) with respect to \(x\).

\(\dfrac{\mathrm{d}}{\mathrm{d}x}e^{7x^2+1}\)\({}=e^{7x^2+1}(14x)\)\({}=14xe^{7x^2+1}\)

Derivatives of Exponential Functions

Derivatives of Exponential Functions

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