To find: The composite function in the form and obtain the derivative of y.
The inner function is and the outer function is .
The derivative of y is .
The function is .
The Chain Rule:
If h is differentiable at x and g is differentiable at , then the composite function defined by is differentiable at x and is given by the product
If n is positive integer, then (2)
Let the inner function be and the outer function be .
Then, and . That is,
Hence, the inner function is and the outer function is .
Thus, the required form of composite function is .
Obtain the derivative of y.
Let and .
Apply the chain rule as shown in equation (1),
The derivative is computed as follows,
Substitute in the above equation,
Thus, the derivative is .
The derivative of is computed as follows,
Apply the power rule as shown in equation (2),
Substitute for and for in equation (3),
Therefore, the derivative of is .
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