Derivative of atan(4x)
Answer
4*(1+16*x^2)^(-1)
Derivative of atan(4x)
- 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: 4*(1+)^(-1)
The derivative of atan(4*x) is 4*(1+16*x^2)^(-1).
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Derivative of atan(4x) = 4*(1+16*x^2)^(-1) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-atan4x
How to find the derivative of atan(4x)
To find the derivative of atan(4x), 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 atan(4x)?▼
The derivative of atan(4x) is 4*(1+16*x^2)^(-1).
How do you find the derivative of atan(4x)?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is 4*(1+16*x^2)^(-1).
Why is the derivative of atan(4x) equal to 4*(1+16*x^2)^(-1)?▼
Because differentiation measures how a function changes — applying the rules to atan(4x) yields 4*(1+16*x^2)^(-1). See the full step-by-step breakdown above.