Attempt 2:9 attempts remaining.
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 Long Gross. in the United States

Mar 30,2025

Question

Attempt 2:9 attempts remaining.
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 Long Gross. in the United States

Mar 30,2025

UpStudy AI · Accepted Answer

We are given the functions

$$
k(s) = 5^3 = 125 \quad \text{and} \quad s(p) = p^3 + 6.
$$

Since $$ k(s) $$ is a constant function, its derivative with respect to its input $$ s $$ is

$$
\frac{dk}{ds} = 0.
$$

Applying the chain rule for the composite function $$ k(s(p)) $$, we have

$$
\frac{dk}{dp} = \frac{dk}{ds} \cdot \frac{ds}{dp}.
$$

Substitute the derivative we found:

$$
\frac{dk}{dp} = 0 \cdot \frac{ds}{dp} = 0.
$$

Thus, the derivative of the composite function is

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