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What is the derivative of f(x) = sin(x^2)?
What is the derivative of f(x) = sin(x^2)?
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Practice Questions
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Q1
What is the derivative of f(x) = sin(x^2)?
2x cos(x^2)
cos(x^2)
2x sin(x^2)
sin(x^2)
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Using the chain rule, f'(x) = cos(x^2) * 2x = 2x cos(x^2).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the derivative of f(x) = sin(x^2)?
Solution:
Using the chain rule, f'(x) = cos(x^2) * 2x = 2x cos(x^2).
Steps: 7
Show Steps
Step 1: Identify the function we want to differentiate, which is f(x) = sin(x^2).
Step 2: Recognize that this is a composite function, where the outer function is sin(u) and the inner function is u = x^2.
Step 3: Apply the chain rule, which states that the derivative of sin(u) is cos(u) multiplied by the derivative of u.
Step 4: Find the derivative of the inner function u = x^2. The derivative is u' = 2x.
Step 5: Now, apply the chain rule: f'(x) = cos(x^2) * (derivative of x^2).
Step 6: Substitute the derivative of the inner function: f'(x) = cos(x^2) * 2x.
Step 7: Simplify the expression to get the final answer: f'(x) = 2x cos(x^2).
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