Derivative of sin(x^2)
Answer
2*cos(x^2)*x
Derivative of sin(x^2)
- 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: os()*x
The derivative of sin(x^2) is 2*cos(x^2)*x.
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How to find the derivative of sin(x^2)
To find the derivative of sin(x^2), 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(x^2)?▼
The derivative of sin(x^2) is 2*cos(x^2)*x.
How do you find the derivative of sin(x^2)?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is 2*cos(x^2)*x.
Why is the derivative of sin(x^2) equal to 2*cos(x^2)*x?▼
Because differentiation measures how a function changes — applying the rules to sin(x^2) yields 2*cos(x^2)*x. See the full step-by-step breakdown above.