Derivative of x^5*cos(x)
Answer
-sin(x)*x^5+5*cos(x)*x^4
Derivative of x^5*cos(x)
- Rule Used
- Product Rule
- Steps
- Identify a product of two functions of x in *: use the product rule (uv)' = u'v + uv'. Each factor is differentiated once while the other is held as-is, then the two terms are added.
- Differentiate each factor and combine.
- Final answer: -*+os(x)*
The derivative of x^5*cos(x) is -sin(x)*x^5+5*cos(x)*x^4.
Instant step-by-step solution for x^5*cos(x)
Share this result
Derivative of x^5*cos(x) = -sin(x)*x^5+5*cos(x)*x^4 Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-x-minus-to-minus-the-minus-5cosx
How to find the derivative of x^5*cos(x)
To find the derivative of x^5*cos(x), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.
Practice More Problems
Derivative of ln(x)
Solve d/dx ln(x)
Derivative of -x
Solve d/dx -x
Derivative of x^(1/2)
Solve d/dx x^(1/2)
Derivative of sqrt(x)
Solve d/dx sqrt(x)
Derivative of x^3
Solve d/dx x^3
Derivative of x*e^x
Solve d/dx x*e^x
Derivative of x*ln(x)
Solve d/dx x*ln(x)
Derivative of x+1
Solve d/dx x+1
Derivative of x^2
Solve d/dx x^2
Frequently Asked Questions
What is the derivative of x^5*cos(x)?▼
The derivative of x^5*cos(x) is -sin(x)*x^5+5*cos(x)*x^4.
How do you find the derivative of x^5*cos(x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is -sin(x)*x^5+5*cos(x)*x^4.
Why is the derivative of x^5*cos(x) equal to -sin(x)*x^5+5*cos(x)*x^4?▼
Because differentiation measures how a function changes — applying the rules to x^5*cos(x) yields -sin(x)*x^5+5*cos(x)*x^4. See the full step-by-step breakdown above.