Derivative of sin(5x)*cos(5x)
Answer
-5*sin(5*x)^2+5*cos(5*x)^2
Derivative of sin(5x)*cos(5x)
- 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: -in()^2+os()^2
The derivative of sin(5*x)*cos(5*x) is -5*sin(5*x)^2+5*cos(5*x)^2.
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Derivative of sin(5x)*cos(5x) = -5*sin(5*x)^2+5*cos(5*x)^2 Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-sin5xcos5x
How to find the derivative of sin(5x)*cos(5x)
To find the derivative of sin(5x)*cos(5x), 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(5x)*cos(5x)?▼
The derivative of sin(5x)*cos(5x) is -5*sin(5*x)^2+5*cos(5*x)^2.
How do you find the derivative of sin(5x)*cos(5x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is -5*sin(5*x)^2+5*cos(5*x)^2.
Why is the derivative of sin(5x)*cos(5x) equal to -5*sin(5*x)^2+5*cos(5*x)^2?▼
Because differentiation measures how a function changes — applying the rules to sin(5x)*cos(5x) yields -5*sin(5*x)^2+5*cos(5*x)^2. See the full step-by-step breakdown above.