Derivative of sin(x)/x^3
Answer
-3*sin(x)*x^(-4)+cos(x)*x^(-3)
Derivative of sin(x)/x^3
- Rule Used
- Quotient Rule
- Steps
- Identify a quotient in /: use the quotient rule (u/v)' = (u'v − uv')/v². The minus sign belongs to the derivative of the denominator; swapping it is the usual error.
- Differentiate numerator and denominator, then combine.
- Final answer: -in(x)*+*
The derivative of sin(x)/x^3 is -3*sin(x)*x^(-4)+cos(x)*x^(-3).
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Derivative of sin(x)/x^3 = -3*sin(x)*x^(-4)+cos(x)*x^(-3) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-sinx-minus-over-minus-x-minus-to-minus-the-minus-3
How to find the derivative of sin(x)/x^3
To find the derivative of sin(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 sin(x)/x^3?▼
The derivative of sin(x)/x^3 is -3*sin(x)*x^(-4)+cos(x)*x^(-3).
How do you find the derivative of sin(x)/x^3?▼
Apply the standard differentiation rules — the key rule used here is the Quotient Rule. The step-by-step result is -3*sin(x)*x^(-4)+cos(x)*x^(-3).
Why is the derivative of sin(x)/x^3 equal to -3*sin(x)*x^(-4)+cos(x)*x^(-3)?▼
Because differentiation measures how a function changes — applying the rules to sin(x)/x^3 yields -3*sin(x)*x^(-4)+cos(x)*x^(-3). See the full step-by-step breakdown above.