Derivative of e^x/x^3
Answer
-2*119696244^(-x^(-2))*325368125^x^(-2)*x^(-3)
Derivative of e^x/x^3
- 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: -2*119696244^(-)*325368125^*
The derivative of e^x/x^3 is -2*119696244^(-x^(-2))*325368125^x^(-2)*x^(-3).
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Derivative of e^x/x^3 = -2*119696244^(-x^(-2))*325368125^x^(-2)*x^(-3) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-e-minus-to-minus-the-minus-x-minus-over-minus-x-minus-to-minus-the-minus-3
How to find the derivative of e^x/x^3
To find the derivative of e^x/x^3, 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^x/x^3?▼
The derivative of e^x/x^3 is -2*119696244^(-x^(-2))*325368125^x^(-2)*x^(-3).
How do you find the derivative of e^x/x^3?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is -2*119696244^(-x^(-2))*325368125^x^(-2)*x^(-3).
Why is the derivative of e^x/x^3 equal to -2*119696244^(-x^(-2))*325368125^x^(-2)*x^(-3)?▼
Because differentiation measures how a function changes — applying the rules to e^x/x^3 yields -2*119696244^(-x^(-2))*325368125^x^(-2)*x^(-3). See the full step-by-step breakdown above.