Can a Function Equal Its Own Derivative?

Axecutioner · Jan 11, 2011

Is it possible for f(x) to be equal to f '(x)? I've been trying all day to make it work and have gotten nothing.

Thanks

rock.freak667 · Jan 11, 2011

Axecutioner said:

Is it possible for f(x) to be equal to f '(x)? I've been trying all day to make it work and have gotten nothing.

Thanks

Sure, if f(x)=e^x, then f'(x) = e^x = f(x).

Axecutioner · Jan 11, 2011

Oh, didn't think about that. XD I kept trying Trig to make it work...

Are there any other ways?

rock.freak667 · Jan 11, 2011

Axecutioner said:

Oh, didn't think about that. XD I kept trying Trig to make it work...

Are there any other ways?

if you solve the differential equation

f'(x)=f(x)

You'd see that any multiply of e^x would satisfy the condition. I think that is the only function, that I know of anyhow.

micromass · Jan 11, 2011

Indeed, every function of the form [tex]f(x)=Ce^x[/tex], with [tex]C\in \mathbb{R}[/tex] will do. There are no other functions that equal it's own derivative...

Can a Function Equal Its Own Derivative?

Discussion

Undergrad Why ##a^0=1##?

Undergrad Finding the minimum distance between two curves

Undergrad Best way to numerically solve this system of equations?

High School Arc Length for Hyperbolic Sin

Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?

Undergrad Correct Upper/Lower limits for continuation of solutions for ODE

Graduate About ellipticity and a proof that a system of PDEs is elliptic

Graduate Leibniz Rule Videos on Digital-University

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Can a Function Equal Its Own Derivative?

Discussion

Similar threads

Undergrad Proving e^x is equals its own derivative?

Graduate Exp(x) is its own derivative (proven axiomatically)

Undergrad Why is e^x its own derivative if e came from compound interest?

When does a periodic function equal its Fourier series?

Graduate How can I numerically solve for f(q) using only its derivative, f'(x)?

Two Functions intersect and have equal derivatives at x=a and x=b

Graduate Can Matter Collapse Its Own Wave Function?

Undergrad Can a Function Be Self-Containing?