∫

Calculus

University

Calculus (University Level)

Derivative of eᵃˣ

Compute the derivative of the exponential function eᵃˣ at a specific x.

Standard Formula

d/dx[eᵃˣ] = a·eᵃˣ

Interactive Sandbox

Live Reactive

Adjust values in real-time and observe mathematical cause-and-effect

Coefficient in exponent(Real number)

0.120

Value of x(Real number)

0.120

Live EquationFormula Proof

d/dx[eᵃˣ] = 1·eᵃˣ = 2.7183

Tangent Line dy/dx

Calculated Solution

2.7183

Direct computational model evaluating Derivative of eᵃˣ.

Variable Mechanics

Roles, constraints & impacts

2 Params

Coefficient in exponent

ImpactPrimary formula parameter

ConstraintReal number

Value of x

ImpactPrimary formula parameter

ConstraintReal number

At a Glance

Gotchas, units & real-world use

Essential

Formula Nature & Mechanics

Direct computational model evaluating Derivative of eᵃˣ.

Common Mistakes & Traps

Ensure all input measurements share consistent units before calculating.
Check for denominator values approaching zero to prevent undefined division.
Follow standard order of operations (PEMDAS: Parentheses, Exponents, Multiply/Divide, Add/Subtract).

Dimensional Analysis & Units

Direct evaluation matching formula variable dimensions.

Real-World & Industry Application

Widely utilized across modern calculus applications, academic analysis, and engineering estimations.

📖 Beginner's guideDerivative of e^x and e^(ax) ExplainedThe derivative of e^(ax) is a·e^(ax), and e^x is its own derivative. Learn why, with examples and common mistakes, plus a free calculator with steps.

Worked Example: Derivative of eᵃˣ

Given:

a = 1
x = 1

d/dx[eˣ] = eˣ
At x=1: e¹ ≈ 2.7183

Answer: 2.7183

Frequently Asked Questions

What is the Derivative of eᵃˣ formula?

d/dx[eᵃˣ] = a·eᵃˣ. Compute the derivative of the exponential function eᵃˣ at a specific x.

How do I calculate Derivative of eᵃˣ?

Enter Coefficient in exponent (a), Value of x (x) into the calculator. It applies d/dx[eᵃˣ] = a·eᵃˣ and shows every step of the working.

Related Calculus Calculators

Power Rule for Derivativesd/dx(xⁿ) = n × x^(n-1)Definite Integral (Power Rule)∫[a to b] x^n dx = [x^(n+1)/(n+1)]|[a to b]Partial Derivative∂f/∂x = lim[h→0] (f(x+h,y) - f(x,y))/h Chain Rule (Derivative)d/dx[f(g(x))] = f'(g(x)) · g'(x)Product Rule (Derivative)d/dx[f·g] = f'·g + f·g'Quotient Rule (Derivative)d/dx[f/g] = (f'·g − f·g') / g²

SponsoredAd

Partner Spotlight

Support free educational math calculators