Yig‘indi va ayirmaning hosilasi mavzusidan test savollari

Agar f(x)= 5sinx+3cosx bo‘lsa, f^{'}( \frac{\pi }{4} ) ni hisoblang

Hosila g^{'}(\frac{\pi }{3}) ni hisoblang.

g(x)=\frac{3x^{2}}{\pi }-2tgx-\pi

Agar g(x)= ctgx+\frac{12x^{3}}{\pi ^{2}}+\pi bo‘lsa, g^{'}(\frac{\pi }{6}) ni hisoblang.

Agar f(x)=2sinx-4\sqrt{3}cosx bo‘lsa, f^{'}(\frac{\pi }{3}) ni hisoblang.

Ushbu y=\frac{1}{3}6^{x}-6 funksiyaning x=1 nuqtadagi hosilasini toping.

f^{'}(\pi ) ni hisoblang.

f(x)=2\cos x- \frac{(\sqrt{\pi })^{3}}{\sqrt{x}}+\frac{\pi }{2}

Agar f(x)=\frac{1}{3}x^{3}-16x bo‘lsa, f^{'}(4) ni toping.

Ushbu y=\sin ^{2}x+\cos ^{2}x funksiyaning hosilasini toping.

f^{'}(\frac{\pi }{6}) ni toping.

f(x)= \sqrt{3}\sin x+\cos \frac{\pi }{3}-\frac{3}{\pi }x^{2}

Ushbu y=tgx\cdot ctgx funksiyaning hosilasini toping.

f^{'}(0) ni hisoblang.

f(x)=x^{3}+3^{x}

y=(x-3)(x^{2}+3x+9) funksiyaning x=3 nuqtadagi hosilasini aniqlang.

Agar f(x)=x^{3}-3x-4 bo‘lsa, \frac{f^{'}(x)}{x-5}\ge 0 tengsizlikni eng kichik butun yechimini toping.

Agar f(x)=x^{3}-1.5x^{2}-6x bo‘lsa, \frac{f^{'}(x)}{x+6}\ge 0 tengsizlikning eng kichik butun yechimini toping.

Agar f(x)=x^{3}-12x+7 bo‘lsa, tengsizlikning eng katta butun yechimini toping.
\frac{f^{'}(x)}{x-4}\le 0

Agarda f(x)=\frac{1}{3}x^{3}+\frac{1}{2}x^{2}-2x+1 bo‘lsa, \begin{cases}{\frac{f^{'}(x)(x+3)}{x^{2}-x-6}\ge 0} \\ {x\le 4} \end{cases} tengsizliklar sistemasining butun yechimlari nechta?

x ning qanday qiymatlarida f(x)=\sin x va g(x)=5x+3 funksiyalar uchunf^{'}(x)<g^{'}(x) tengsizlik bajariladi?

Ushbu f(x)=\frac{1}{3}x^{3}+\frac{3}{2}x^{2}-4x bo‘lsa, \begin{cases}{\frac{f^{'}(x)(x-1)}{x^{2}-x-6}\le 0}\\{x\ge -4} \end{cases} tengsizliklar sistemasining butun yechimlari nechta?

x ning qanday qiymatlarida f(x)=\frac{1}{3}x^{3} va g(x)=-x^{2}+3x funksiyalar uchun f^{'}(x)<g^{'}(x) tengsilik o‘rinli bo‘ladi?

Agar f(x)=-4x^{3}-11x^{2}-8x+7 bo‘lsa, f^{'}(x)\ge 0 tengsizlikning nechta butun yechimi bor?

Ushbu y=2^{x}-1 funksiyaning x=1 nuqtadagi hosilasini toping.

Agar f(x)=x^{\frac{2}{3}}+85\frac{1}{3}\ln x bo‘lsa, f^{'}(8) ning qiymatini toping.

Agar f(x)=16x^{3}-24x^{2}+9x-1 bo‘lsa, \frac{f^{'}(x)}{x^{2}}\le 0 tengsizlikning butun sonlardan iborat nechta yechimi bor?

Agar \phi ^{'}(x)=\ln x bo‘lsa, x ning \phi ^{'}(x)+\phi (x)=\frac{1}{x}-\phi (\frac{1}{x}) tengsizlikni qanoatlantiradigan barcha qiymatlarini toping.

Agar f(x)=3x+\frac{3}{x} bo‘lsa, f^{'}(x)<0 tengsizlikni yeching.

Nechta nuqtada f(x)=x^{3} funksiya va uning hosilasi qiymatlari teng bo‘ladi?

Agar f(x)=x^{2}+|x| bo‘lsa, f^{'}(-1) ni toping.

\cos x\ge (-\frac{\pi }{2}x)' tengsizlikni yeching.

Agar f(x)=x^{3}+x-\sqrt{2} va g(x)=3x^{2}+x+\sqrt{2} bo‘lsa, f^{'}(x)>g^{'}(x) tengsizlikning eng kichik natural yechimini toping.

Agar y=4-\sqrt[3]{x^{2}} bo‘lsa, y^{'}(-\frac{8}{27}) ni hisoblang.