$$
g(x)=6 x^{3} \sqrt{x} \csc (x)
$$

Which sequence of rules can be used in order to differentiate $g$ in its current form?

Choose 1 answer:
(A) Chain rule, then product rule
(B) Product rule, then product rule again
(C) Product rule, then chain rule
(D) Chain rule, then chain rule again

Question

$$
g(x)=6 x^{3} \sqrt{x} \csc (x)
$$

Which sequence of rules can be used in order to differentiate $g$ in its current form?

Choose 1 answer:
(A) Chain rule, then product rule
(B) Product rule, then product rule again
(C) Product rule, then chain rule
(D) Chain rule, then chain rule again

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the function to differentiate: $g(x)=6x^3\sqrt{x}\csc(x)$. ‖ ‖ step 2 ⋮ Recognize that $g(x)$ is a product of three functions: $6x^3$, $\sqrt{x}$, and $\csc(x)$. ‖ ‖ step 3 ⋮ Apply the product rule to differentiate the product of these three functions. ‖ ‖ step 4 ⋮ After applying the product rule, notice that the resulting terms may require the use of the chain rule to differentiate functions like $\sqrt{x}$ and $\csc(x)$. ‖ ‖ step 5 ⋮ The differentiation process will involve both the product rule and the chain rule, as seen in the asksia-ll calculation. ‖ ***C*** ∻Key Concept∻ ⚹Product and Chain Rules in Differentiation⚹ ∻Explanation∻ ⚹To differentiate a product of functions, the product rule is used first. If the resulting terms are composite functions,◊What is the product rule in calculus and how is it applied to differentiate a function?⍭ Generate me a similar question◊⚹

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