Derivative of tan(x)^5
Answer
5*sec(x)^2*tan(x)^4
Derivative of tan(x)^5
- 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(x)^an(x)^4
The derivative of tan(x)^5 is 5*sec(x)^2*tan(x)^4.
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Derivative of tan(x)^5 = 5*sec(x)^2*tan(x)^4 Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-tanx-minus-to-minus-the-minus-5
How to find the derivative of tan(x)^5
To find the derivative of tan(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 tan(x)^5?▼
The derivative of tan(x)^5 is 5*sec(x)^2*tan(x)^4.
How do you find the derivative of tan(x)^5?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is 5*sec(x)^2*tan(x)^4.
Why is the derivative of tan(x)^5 equal to 5*sec(x)^2*tan(x)^4?▼
Because differentiation measures how a function changes — applying the rules to tan(x)^5 yields 5*sec(x)^2*tan(x)^4. See the full step-by-step breakdown above.