Derivative of e^(3x)
Answer
3*e^(3*x)
Derivative of e^(3x)
- Rule Used
- Chain Rule
- Steps
- Identify a composite function in : use the chain rule = f'(g(x))·g'(x). The inner derivative is required because a stretch or shift of the input changes how fast the output moves.
- Differentiate the outer function, then multiply by the inner derivative.
- Final answer:
The derivative of e^(3*x) is 3*e^(3*x).
Instant step-by-step solution for e^(3x)
Share this result
Derivative of e^(3x) = 3*e^(3*x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-e-minus-to-minus-the-minus-3x
How to find the derivative of e^(3x)
To find the derivative of e^(3x), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.
Practice More Problems
Derivative of x*ln(x)
Solve d/dx x*ln(x)
Derivative of x+1
Solve d/dx x+1
Derivative of x*sin(x)
Solve d/dx x*sin(x)
Derivative of x^2
Solve d/dx x^2
Derivative of x^2-1
Solve d/dx x^2-1
Derivative of x^2+1
Solve d/dx x^2+1
Derivative of x^4
Solve d/dx x^4
Derivative of 10^x
Solve d/dx 10^x
Derivative of 2^x
Solve d/dx 2^x
Derivative of e^(2x)
Solve d/dx e^(2x)
Frequently Asked Questions
What is the derivative of e^(3x)?▼
The derivative of e^(3x) is 3*e^(3*x).
How do you find the derivative of e^(3x)?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is 3*e^(3*x).
Why is the derivative of e^(3x) equal to 3*e^(3*x)?▼
Because differentiation measures how a function changes — applying the rules to e^(3x) yields 3*e^(3*x). See the full step-by-step breakdown above.