Derivative of tan(5x)
Answer
5*sec(5*x)^2
Derivative of tan(5x)
- Rule Used
- Chain Rule
- Steps
- Identify a composite function in : use the chain rule = f'(g(x))·g'(x). The inner derivative is required because a stretch or shift of the input changes how fast the output moves.
- Differentiate the outer function, then multiply by the inner derivative.
- Final answer: ec()^2
The derivative of tan(5*x) is 5*sec(5*x)^2.
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How to find the derivative of tan(5x)
To find the derivative of tan(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 tan(5x)?▼
The derivative of tan(5x) is 5*sec(5*x)^2.
How do you find the derivative of tan(5x)?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is 5*sec(5*x)^2.
Why is the derivative of tan(5x) equal to 5*sec(5*x)^2?▼
Because differentiation measures how a function changes — applying the rules to tan(5x) yields 5*sec(5*x)^2. See the full step-by-step breakdown above.