Respuesta :

annaboglino

Answer:

D

Step-by-step explanation:

Here we just need to plug in x² into the t values and then multiply by the derivative of x²

  • [tex](\frac{sin(x^{2} )}{x^{2} } )(2x) = \frac{2sin(x^{2} )}{x}[/tex]
sqdancefan

Answer:

  [tex]\textbf{D. }f'(x)=\dfrac{2\sin{(x^2)}}{x}[/tex]

Step-by-step explanation:

The fundamental rule of calculus tells you when ...

  [tex]f(x)=\displaystyle\int_a^u{g(t)\,dt}\\\\f'(x)=g(u)u'[/tex]

We have g(t) = sin(t)/t, and u(x) = x^2, so ...

  [tex]f'(x)=\dfrac{\sin{(x^2)}}{x^2}(2x)=\dfrac{2\sin{(x^2)}}{x} \qquad\text{matches D}[/tex]

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