Derivative of e^(5x-1)
Answer
5*119696244^(-5*x+1)*325368125^(-1+5*x)
Derivative of e^(5x-1)
- 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: 5*119696244^(-+1)*325368125^(-1+)
The derivative of e^(5*x-1) is 5*119696244^(-5*x+1)*325368125^(-1+5*x).
Instant step-by-step solution for e^(5x-1)
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Derivative of e^(5x-1) = 5*119696244^(-5*x+1)*325368125^(-1+5*x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-e-minus-to-minus-the-minus-5x-minus-1
How to find the derivative of e^(5x-1)
To find the derivative of e^(5x-1), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.
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Frequently Asked Questions
What is the derivative of e^(5x-1)?▼
The derivative of e^(5x-1) is 5*119696244^(-5*x+1)*325368125^(-1+5*x).
How do you find the derivative of e^(5x-1)?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is 5*119696244^(-5*x+1)*325368125^(-1+5*x).
Why is the derivative of e^(5x-1) equal to 5*119696244^(-5*x+1)*325368125^(-1+5*x)?▼
Because differentiation measures how a function changes — applying the rules to e^(5x-1) yields 5*119696244^(-5*x+1)*325368125^(-1+5*x). See the full step-by-step breakdown above.