ddxeu=eu dudx The natural exponential reproduces itself under differentiation; composition adds the inner-rate multiplier. Method Keep the exponential unchanged and multiply by the derivative of its exponent. For a sum, differentiate each term. Example y=2e-3x, dydx=-6e-3x Exam check Never reduce the exponent by one as if this were a power of the input. A negative exponent derivative can make the gradient negative.

\(\dfrac{\mathrm{d}}{\mathrm{d}x}e^{u}=e^u\dfrac{\mathrm{d}u}{\mathrm{d}x}\)

The natural exponential reproduces itself under differentiation; composition adds the inner-rate multiplier.

Keep the exponential unchanged and multiply by the derivative of its exponent. For a sum, differentiate each term.

\(y=2e^{-3x},\quad\dfrac{\mathrm{d}y}{\mathrm{d}x}=-6e^{-3x}\)

Never reduce the exponent by one as if this were a power of the input. A negative exponent derivative can make the gradient negative.

Natural exponential derivatives

Natural exponential derivatives