What is (d^2)/(dx^2)(e^{rx}) ?

The answer to (d^2)/(dx^2)(e^{rx}) is e^{xr}(x(dr)/(dx)+r)^2+e^{xr}(x(d^2r)/(dx^2)+2(dr)/(dx))

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(d^2)/(dx^2)(e^{rx})

\frac{d ^{2}}{d x ^{2}} (e^{r x})

e^{x r} (x \frac{d r}{d x} + r)^{2} + e^{x r} (x \frac{d ^{2} r}{d x ^{2}} + 2 \frac{d r}{d x})

Solution steps

\frac{d ^{2}}{d x ^{2}} (e^{r x})

\frac{d}{d x} (e^{r x}) = e^{r x} (x \frac{d r}{d x} + r)

= \frac{d}{d x} (e^{r x} (x \frac{d r}{d x} + r))

\frac{d}{d x} (e^{r x} (x \frac{d r}{d x} + r)) = e^{x r} (x \frac{d r}{d x} + r)^{2} + e^{x r} (x \frac{d ^{2} r}{d x ^{2}} + 2 \frac{d r}{d x})

= e^{x r} (x \frac{d r}{d x} + r)^{2} + e^{x r} (x \frac{d ^{2} r}{d x ^{2}} + 2 \frac{d r}{d x})

\frac{x ^{\frac{1}{2}}}{( x + 1 ) ^{\frac{1}{2}}}

12 e^{- 2}

2^{n}

\frac{1}{2 π} e^{- 0.5 (2)^{2}}

7 \cdot 1 0^{- 3} \cdot \frac{0.5715}{1 0 ^{- 6}}

What is (d^2)/(dx^2)(e^{rx}) ?
The answer to (d^2)/(dx^2)(e^{rx}) is e^{xr}(x(dr)/(dx)+r)^2+e^{xr}(x(d^2r)/(dx^2)+2(dr)/(dx))