فرمول های رایج مشتق (Derivative)، در ریاضیات (Mathematics)
مقدار ثابت (Constant) :
\[ {d \over {dx}}\left( c \right) = 0 \]مجموع (Sum) :
\[ {d \over {dx}}\left( {u + v} \right) = {{du} \over {dx}} + {{dv} \over {dx}} \]تفاضل (Difference) :
\[ {d \over {dx}}\left( {u - v} \right) = {{du} \over {dx}} - {{dv} \over {dx}} \]مضرب ثابت (Constant Multiple) :
\[ {d \over {dx}}\left( {cu} \right) = c{{du} \over {dx}} \]حاصل ضرب (Product) :
\[ {d \over {dx}}\left( {uv} \right) = u{{dv} \over {dx}} + v{{du} \over {dx}} \] \[ {\left[ {f\left( x \right)g\left( x \right)} \right]^\prime } = {f^\prime }\left( x \right)g\left( x \right) + f\left( x \right){g^\prime }\left( x \right) \]خارج قسمت (Quotient) :
\[ {d \over {dx}}\left( {{u \over v}} \right) = {{v{{du} \over {dx}} - u{{dv} \over {dx}}} \over {{v^2}}} \]توان (Power) :
\[ {d \over {dx}}{x^n} = n{x^{n - 1}} \]قاعده زنجیری (Chain Rule) :
\[ {d \over {dx}}\left( {f\left( {g\left( x \right)} \right)} \right) = {f^\prime }\left( {g\left( x \right)} \right).{g^\prime }\left( x \right) \]
\[ {d \over {dx}}{a^x} = {a^x}\ln a \] \[ {d \over {dx}}\left( {{a^u}} \right) = {a^u}\ln a{{du} \over {dx}} \] \[ {d \over {dx}}\left( {{a^{f\left( x \right)}}} \right) = {a^{f\left( x \right)}}\ln a {f^\prime }\left( x \right) \] \[ {d \over {dx}}\left( {{u^n}} \right) = n{u^{n - 1}}{{du} \over {dx}} \] \[ {d \over {dx}}\left( {{{\left( {f\left( x \right)} \right)}^n}} \right) = n{\left( {f\left( x \right)} \right)^{n - 1}}{f^\prime }\left( x \right) \]
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Thomas' Calculus Early Transcendentals - George B. Thomas Jr., Maurice D. Weir, Joel R. Hass - 13th Edition
نویسنده علیرضا گلمکانی
شماره کلید 10094
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