Consider the functions f(x) = x^3 and g(x) = 2x.
Which of the following choices below shows the correct use of the chain rule to find the derivative of the composition function $\big(f \circ g\big)(x)$ \big(f \circ g\big)(x), that is, for $\big(f \circ g\big)'(x)$ \big(f \circ g\big)'(x)?

Question

Consider the functions f(x) = x^3 and g(x) = 2x.

Which of the following choices below shows the correct use of the chain rule to find the derivative of the composition function $\big(f \circ g\big)(x)$ \big(f \circ g\big)(x), that is, for $\big(f \circ g\big)'(x)$ \big(f \circ g\big)'(x)?

Answer

\big(f \circ g\big)'(x) = 3x^2\, 2 = 6x^2

Answer

\big(f \circ g\big)'(x) = 3(2x)^2 \,2 = 24x^2

Answer

\big(f \circ g\big)'(x) = 3(2x)^2 \,2x = 24x^3

Answer

\big(f \circ g\big)'(x) = 3(2x^2) \,2 = 12x^2

Answer

\big(f \circ g\big)'(x) = 3x^2\, 2x = 6x^3

Crowdly

Consider the functions f(x) = x^3 and g(x) = 2x . Which of the followi...

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