question 6 of 11, step 1 of 2 consider the following function: f(s, t)=s³ + 14s³t⁴+3st³ + 19 step 1 of 2…
question 6 of 11, step 1 of 2 consider the following function: f(s, t)=s³ + 14s³t⁴+3st³ + 19 step 1 of 2: find ∂f/∂s. answer ∂f/∂s =
Answer
Explanation:
Step1: Differentiate term - by - term
When differentiating $s^{3}$ with respect to $s$, using the power rule $\frac{d}{ds}(s^{n})=ns^{n - 1}$, we get $3s^{2}$.
Step2: Differentiate $14s^{3}t^{4}$ with respect to $s$
Treat $t$ as a constant. Using the power rule, $\frac{d}{ds}(14s^{3}t^{4})=14t^{4}\frac{d}{ds}(s^{3}) = 42s^{2}t^{4}$.
Step3: Differentiate $3st^{3}$ with respect to $s$
Treat $t$ as a constant. Using the power rule, $\frac{d}{ds}(3st^{3})=3t^{3}$.
Step4: Differentiate the constant
The derivative of a constant 19 with respect to $s$ is 0.
Answer:
$3s^{2}+42s^{2}t^{4}+3t^{3}$