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find the first derivative of
Full solution
Q. find the first derivative of
- Identify Function: Identify the function to differentiate.We are given the function and we need to find its first derivative, .
- Apply Chain Rule: Apply the chain rule for differentiation.The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. In this case, the outer function is and the inner function is .
- Differentiate Outer Function: Differentiate the outer function with respect to the inner function.The derivative of with respect to is .
- Differentiate Inner Function: Differentiate the inner function with respect to . The derivative of with respect to is .
- Apply Chain Rule Result: Apply the chain rule by multiplying the results from Step and Step .
- Simplify Final Answer: Simplify the expression if necessary.The expression is already simplified, so we have the final answer.
