What is the derivative of $\frac{sin (x)}{x}$ $sin(x)/x$ ?

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Answer 1 · 2016-06-14T20:13:27

$\frac{x cos (x) - sin (x)}{x^{2}}$ $(xcos(x)-sin(x))/x^2$

To find the derivative of a function in the form $\frac{f (x)}{g (x)}$ $f(x)/g(x)$ , use the quotient rule:

$d/dx(f(x)/g(x))=(f^'(x)g(x)-g^'(x)f(x))/(g(x))^2$

For the function $sin(x)/x$ , we see that:

$f(x)=sin(x)" "=>" "f^'(x)=cos(x)$

$g(x)=x" "=>" "g^'(x)=1$

Plugging these into the quotient rule, we see that:

$d/dx(sin(x)/x)=(cos(x)*x-1*sin(x))/x^2$

$=(xcos(x)-sin(x))/x^2$

Answer 2 · 2016-06-14T20:22:23

$(xcosx-sinx)/x^2.$

Rule : $d/dx(f(x)/g(x))=(g(x)*f'(x)-f(x)*g'(x))/(g(x))^2$

$:. d/dx (sinx/x) ={x*(sinx)'-(sinx)(x)'}/x^2=(xcosx-sinx)/x^2.$

What is the derivative of sin(x)/xsin(x)xsin(x)/x?