Question

знайти похідну функції

Answer 1

$a) f'(x)=4x^3-1+dfrac{2x}{2sqrt{x^2+1}}=4x^3-1+dfrac{x}{sqrt{x^2+1}}\ b) f'(x)=(e^{2x})'cosdfrac x2+e^{2x}left(cosdfrac x2right)'+2,mathrm{tg},xcdotdfrac{1}{cos^2x}=\ =2e^{2x}cosdfrac x2-dfrac12e^{2x}sindfrac x2+dfrac{2,mathrm{tg}, x}{cos^2x}\ c) f'(x)=dfrac{(2x+sin x)(x+sin x)-(1+cos x)(x^2-cos x)}{(x+sin x)^2}-dfrac2{x^2}+\+5\ d) f'(x)=5left(1-dfrac1{2x}right)^4cdotdfrac1{2x^2}+2sin xcos x$