Тест по теме "Производная тригонометрических, показательных и логарифмических функций"

\(f'\left(x\right)=6\cos x+6\sin x\)

\(f'\left(x\right)=6\cos x-6\sin6x\)

\(f'\left(x\right)=6\cos x-\sin6x\)

\(\left(\cos\ x\right)'=\sin\ x\)

\(\left(\sin\ x\right)'=-\ \cos\ x\)

\(\left(tg\ x\right)'=\frac{1}{\cos^2x}\)

\(\left(\operatorname{ctg}\ x\right)'=\frac{1}{\sin^2x}\)

\(\left(e^x\right)'=e^x\)

\(\left(\ln\ x\right)'=\frac{1}{x}\)

\(\left(a^x\right)'=\frac{a^x}{\ln a}\)

\(\left(\log_ax\right)'=\frac{1}{x\ln a}\)

\(f'\left(x\right)=\frac{2}{x}+5^x\ln5+3e^{3x}\)

\(f'\left(x\right)=2x+5^x\ln5+e^{3x}\)

\(f'\left(x\right)=\frac{2}{\ln x}+5^x+3e^x\)

\(f'\left(x\right)=\cos^3x\)

\(f'\left(x\right)=3\cos^2x\ \sin x\)

\(f'\left(x\right)=3\sin^2x\ \cos x\)

\(f'\left(x\right)=\cos^{ }x^2\)

\(f'\left(x\right)=2x\cos^{ }x^2\ \)

\(f'\left(x\right)=2\sin^2x\ \cos x\)

\(f'\left(x\right)=-\frac{\sin x}{2}\)

\(f'\left(x\right)=\frac{x}{2}\cos^{ }\frac{x}{2}\ \)

\(f'\left(x\right)=2\sin^{ }x\ \cos x\)

\(f'\left(x\right)=x\left(2\cos x-x\sin x\right)\)

\(f'\left(x\right)=-2x\ \sin x\)

\(f'\left(x\right)=2x\sin^{ }x\ +2x\cos x\)