Pregunta
For the composite function
, identify an inside and outside function. Write the derivative of the composite function with respect to
. Do not use identity functions for
or
.
Ask by Stewart Little. in the United States
Mar 31,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The inside function is
and the outside function is
where
. The derivative of the composite function is
.
Solución

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Como
The Deep Dive
In the composite function
, the inside function is
, which takes the input
and produces an output that becomes the input for the outside function
. The outside function is
, where
.
To find the derivative of the composite function
with respect to
, we apply the chain rule. The derivative is given by:
Here,
represents the derivative of the outside function evaluated at the inside function, and
is the derivative of the inside function.

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