Question number 1.


ddx(f(g(x)))
 =
f′(g(x))⋅g′(x)



f(g(x))⋅g′(x)



f′(g′(x))



f(g′(x))⋅f′(x)



None of the above.

The correct derivative of the composition of two functions, \( f(g(x)) \), is found using the **chain rule**. The chain rule states:

\[
\frac{d}{dx}(f(g(x))) = f'(g(x)) \cdot g'(x)
\]

So the correct answer is:

\[
f'(g(x)) \cdot g'(x)
\]

Thus, the first option is correct.

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Would you like further explanation on this? Here are some related questions:

1. What is the chain rule in calculus, and how is it applied?
2. Can you solve a problem involving the chain rule with trigonometric functions?
3. How do you differentiate a product of functions, and is the chain rule applicable?
4. How does the chain rule extend to functions of multiple variables?
5. What is the difference between the chain rule and the product rule in differentiation?

**Tip:** When applying the chain rule, always remember to differentiate the "outer" function first, followed by the derivative of the "inner" function.

ddx(f(g(x))) = f′(g(x))⋅g′(x) f(g(x))⋅g′(x) f′(g′(x)) f(g′(x))⋅f′(x) None of the above.

Learn how to differentiate composite functions using the chain rule. This example demonstrates the correct application of the chain rule to ddx(f(g(x))) with a detailed explanation, suitable for advanced high school students and college-level calculus learners.

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ddx(f(g(x)))

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