Attempt $$ 5: 6 $$ attempts remaining. Find the derivative of the composite function $$ k(d(p)) $$ in terms of one input variable for the pair of functions $$ k(s) $$ and $$ s(p) $$. Be sure to use the correct variable as the independent variable. $$ k(s)=5^{s} ; \quad s(p)=p^{3}+6 $$ $$ \frac{d k}{d p}= $$

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We are given the functions
$$
k(s)=5^{s} \quad \text{and} \quad s(p)=p^{3}+6.
$$
We want to find the derivative of the composite function $$ k(s(p)) $$ with respect to $$ p $$.

**Step 1.** Identify the composite function:
$$
k(s(p)) = 5^{s(p)} = 5^{p^3+6}.
$$

**Step 2.** Differentiate using the chain rule. The chain rule states that:
$$
\frac{dk}{dp}=\frac{dk}{ds}\cdot\frac{ds}{dp}.
$$

**Step 3.** Compute $$\frac{dk}{ds}$$. Since 
$$
k(s)=5^s,
$$
the derivative with respect to $$ s $$ is
$$
\frac{dk}{ds}=5^s\ln 5.
$$

**Step 4.** Compute $$\frac{ds}{dp}$$. We have
$$
s(p)=p^3+6,
$$
thus its derivative is
$$
\frac{ds}{dp}=3p^2.
$$

**Step 5.** Combine the results using the chain rule:
$$
\frac{dk}{dp}=5^s\ln5\cdot 3p^2.
$$
Replacing $$ s $$ with $$ s(p)=p^3+6 $$ gives:
$$
\frac{dk}{dp}=5^{p^3+6}\ln5\cdot 3p^2.
$$

Thus, the derivative is:
$$
\frac{dk}{dp}=3p^2\ln5\,5^{p^3+6}.
$$
The derivative of $$ k(s(p)) $$ with respect to $$ p $$ is $$ 3p^2 \ln 5 \times 5^{p^3+6} $$.

Attempt 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.

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Attempt 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.