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almond37 [142]
4 years ago
13

What function do you know from calculus is such that its first derivative is itself? (Do not use the function f(x) = 0.)

Mathematics
1 answer:
stiks02 [169]4 years ago
7 0

Answer:

f(x)=e^x

Step-by-step explanation:

Proof:

Let e^x=z

take logs in both sidesln(e^x)=ln(z)

using log properties we have xln(e)=ln(z). We know that ln(e)=1 then x=ln(z)

Taking derivatives with respect to x, we have: 1=\frac{1}{z}\frac{dz}{dx}

Next we can move things around z=\frac{dz}{dx}

Replacing z for e^x as defined in the first line, we get

e^x=\frac{d}{dx}e^x

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