WebOct 17, 2024 · What function has a derivative that is equal to 3x2? One such function is y = x3, so this function is considered a solution to a differential equation. Definition: differential equation A differential … WebDec 1, 2024 · The derivative of e to the x with respect to the variable x is equal to -3e-3x. It is denoted by d/dx (e -3x ). It is the rate of change of the exponential function e and it is always equal to the exponential function itself.

Antiderivative Calculator - Symbolab

WebAn antiderivative of function f (x) is a function whose derivative is equal to f (x). Is integral the same as antiderivative? The set of all antiderivatives of a function is the indefinite integral of the function. The difference between any two functions in the set is a constant. WebOct 2, 2024 · Derivative of e 3x Formula. The derivative of e 3x is 3e 3x. Mathematically, we can express it as . d/dx(e 3x) = 3e 3x or (e 3x)’ = 3e 3x. What is the derivative of e 3x? … the businessman movie

Taking the derivative of e^3x Physics Forums

WebAnswer (1 of 2): Im guessing you're asking why d/dx((1/3)e^3x) = e^3x and not e^2x. It's because you missed a step in the chain rule where you multiply by the derivative of the variable you replaced. In other words: (1/3)e^3x = (1/3)(e^x)^3 d/dx((1/3)e^3x) = d/dx((1/3)(e^x)^3) d/dx((1/3)e^3x) = ... Web3*E^(3*x) - sin(x) + 1. Detail solution Differentiate term by term: Differentiate term by term: The derivative of a constant times a function is the constant times the derivative of the function. Let . The derivative of is itself. Then, apply the chain rule. Multiply by : Webe^x times 1. f' (x)= e^ x : this proves that the derivative (general slope formula) of f (x)= e^x is e^x, which is the function itself. In other words, for every point on the graph of f (x)=e^x, the slope of the tangent is equal to the y-value of tangent point. So if y= 2, slope will be 2. if y= 2.12345, slope will be 2.12345. tastiest tumbler cherry tomatoes