Find the derivative of the composite function in terms of one input variable for the pair of functions and . Be sure to use the correct variable
as the independent variable.

Ask by Cruz Bob. in the United States

Mar 30,2025

Question

Find the derivative of the composite function in terms of one input variable for the pair of functions and . Be sure to use the correct variable
as the independent variable.

Ask by Cruz Bob. in the United States

Mar 30,2025

UpStudy AI · Accepted Answer

We are given
$$
k(s)=5^{2}=25 \quad \text{and} \quad s(p)=p^{3}+6.
$$
Since $$ k(s) $$ is a constant function (it always equals $$ 25 $$), its derivative with respect to $$ s $$ is zero:
$$
k'(s)=0.
$$

Now, consider the composite function:
$$
k(s(p))=25.
$$
Using the chain rule, we have:
$$
\frac{d}{dp}k(s(p)) = k'(s(p)) \cdot s'(p).
$$
Substitute $$ k'(s(p))=0 $$ into the expression:
$$
\frac{d}{dp}k(s(p)) = 0 \cdot s'(p) = 0.
$$

Thus, the derivative is:
$$
\frac{dk}{dp}=0.
$$
The derivative of $$ k(d(p)) $$ with respect to $$ p $$ is 0.

Find the derivative of the composite function in terms of one input variable for the pair of functions and . Be sure to use the correct variable
as the independent variable.

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Find the derivative of the composite function in terms of one input variable for the pair of functions and . Be sure to use the correct variable as the independent variable.

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Find the derivative of the composite function in terms of one input variable for the pair of functions and . Be sure to use the correct variable
as the independent variable.