найти производную функции: 1) (3x^2-1/x^3) 2) (x/3+7)^6 ,3) e^x cos x , 4) 2^x/sin x. Created by Zoomka. algebra-ru

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найти производную функции: 1) (3x^2-1/x^3) 2) (x/3+7)^6 ,3) e^x cos x , 4) 2^x/sin x

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sergio8800

Verified answer

$(3x^2-\frac{1}{x^3})'=(3x^2)'-(\frac{1}{x^3})'=6x+\frac{3}{x^4}$

$((\frac{x}{3}+7)^6)'=6(\frac{x}{3}+7)^5(\frac{x}{3}+7)'=\frac{6(\frac{x}{3}+7)^5}{3}=2(\frac{x}{3}+7)^5$

$(e^xcosx)'=(e^x)'cosx+e^x(cosx)'=e^xcosx-e^xsinx=e^x(cosx-sinx)$

$(\frac{2^x}{sinx})'=\frac{(2^x)'sinx-2^x(sinx)'}{sin^2x}=\frac{2^xln2sinx-2^xcosx}{sin^2x}=2^x\frac{ln2-ctgx}{sinx}$

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pomogite kto dast vse reshenie polnostyu tochno vyberu luchshim otvetom 1 plosh

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