Derivative of sin(x)/x^5

Answer

-\frac{5 \cdot \mathrm{sin}\left(x\right)}{x^{6}}+\frac{\mathrm{cos}\left(x\right)}{x^{5}}

Derivative of sin(x)/x^5

Rule Used: Quotient Rule
Steps: Identify a quotient in $\sin(x)$ / $x^5$ : 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: - $5 \cdot s$ in(x)* $x^{-6}$ + $\cos(x)$ * $x^{-5}$

The derivative of sin(x)/x^5 is -5*sin(x)*x^(-6)+cos(x)*x^(-5).

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Derivative of sin(x)/x^5 = -5*sin(x)*x^(-6)+cos(x)*x^(-5) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-sinx-minus-over-minus-x-minus-to-minus-the-minus-5

How to find the derivative of sin(x)/x^5

To find the derivative of sin(x)/x^5, 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^5?▼

The derivative of sin(x)/x^5 is -5*sin(x)*x^(-6)+cos(x)*x^(-5).

How do you find the derivative of sin(x)/x^5?▼

Apply the standard differentiation rules — the key rule used here is the Quotient Rule. The step-by-step result is -5*sin(x)*x^(-6)+cos(x)*x^(-5).

Why is the derivative of sin(x)/x^5 equal to -5*sin(x)*x^(-6)+cos(x)*x^(-5)?▼

Because differentiation measures how a function changes — applying the rules to sin(x)/x^5 yields -5*sin(x)*x^(-6)+cos(x)*x^(-5). See the full step-by-step breakdown above.

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