Derivative of sin(x)/x^4
Answer
-4*sin(x)*x^(-5)+cos(x)*x^(-4)
Derivative of sin(x)/x^4
- 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^4 is -4*sin(x)*x^(-5)+cos(x)*x^(-4).
Instant step-by-step solution for sin(x)/x^4
Share this result
Derivative of sin(x)/x^4 = -4*sin(x)*x^(-5)+cos(x)*x^(-4) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-sinx-minus-over-minus-x-minus-to-minus-the-minus-4
How to find the derivative of sin(x)/x^4
To find the derivative of sin(x)/x^4, we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.
Practice More Problems
Derivative of cosh(x)
Solve d/dx cosh(x)
Derivative of cot(x)
Solve d/dx cot(x)
Derivative of csc(x)
Solve d/dx csc(x)
Derivative of sec(x)
Solve d/dx sec(x)
Derivative of sin(2x)
Solve d/dx sin(2x)
Derivative of sin(x)^2
Solve d/dx sin(x)^2
Derivative of sin(x)
Solve d/dx sin(x)
Derivative of sinh(x)
Solve d/dx sinh(x)
Derivative of tan(x)^2
Solve d/dx tan(x)^2
Derivative of tan(x)
Solve d/dx tan(x)
Frequently Asked Questions
What is the derivative of sin(x)/x^4?▼
The derivative of sin(x)/x^4 is -4*sin(x)*x^(-5)+cos(x)*x^(-4).
How do you find the derivative of sin(x)/x^4?▼
Apply the standard differentiation rules — the key rule used here is the Quotient Rule. The step-by-step result is -4*sin(x)*x^(-5)+cos(x)*x^(-4).
Why is the derivative of sin(x)/x^4 equal to -4*sin(x)*x^(-5)+cos(x)*x^(-4)?▼
Because differentiation measures how a function changes — applying the rules to sin(x)/x^4 yields -4*sin(x)*x^(-5)+cos(x)*x^(-4). See the full step-by-step breakdown above.