Question

find the derivative of f(x)=sinx/x​

Answer 1

Answer:

f(x)=sinx/x

f'(x)= x (sin'x) - sinx(x')/x²

=> xcosx-sinx/x²

hope it helps

Answer 2

☯ Explanation,

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$\bigstar \rm \: f(x) = \dfrac{sin \: (x)}{x} \\ \\ \\ \rm \leadsto \:f'(x) = \dfrac{d}{dx} ( \dfrac{sin \: (x)}{x} ) \\ \\ \\ \rm\underline{ \red{Using \: differentiation \: rule, }}\\ \\ \\ \rm \leadsto \:f'(x) = \dfrac{ \dfrac{d}{dx} (sin \: (x)) \times x - sin \: (x) \times \dfrac{d}{dx} (x)}{x {}^{2} } \\ \\ \\ \rm \leadsto \:f'(x) = \dfrac{cos \: (x)\times x - sin \:( x) \times \dfrac{d}{dx} (x)}{x {}^{2} } \\ \\ \\ \rm \leadsto \:f'(x) = \dfrac{cos \: (x )\times x - sin \:( x )\times 1}{x {}^{2} } \\ \\ \\ \leadsto \underline{ \boxed{\rm \:f'(x) = \dfrac{cos \:( x) \times x - sin \:( x )}{x {}^{2} }}} \: \bigstar$

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☯ Know to more,

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$\bull \rm \: Power \: Rule: ( \dfrac{d}{dx}) (x {}^{n}  ) = nx {}^{n - 1} \\ \\ \\ \bull\rm \: Derivative \: of \: a \: constant, \: a:  \: ( \dfrac{d}{dx}) (a) = 0 \\ \\ \\ \bull\rm \: Derivative \: of \: a \: constant \: multiplied \: with \: function \: f: ( \dfrac{d}{dx}) (a. f) = af'  \\ \\ \\ \\ \bull \rm Sum \: Rule: ( \dfrac{d}{dx}) (f  \pm g) = f' \pm \: g' \\ \\ \\ \bull\rm Product \: Rule: ( \dfrac{d}{dx}) (fg)= fg' + gf' \\ \\ \\ \bull\rm \: Quotient \: Rule: \dfrac{d}{dx}( \dfrac{f}{g}) = \dfrac{gf'- fg'}{g {}^{2} }$

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