গুণফল ,ভাগফল ও সংযোজিত ফাংশনের অন্তরজ/Chain Rule
h(x)=ln(emx+e−mx) h \left ( x \right ) = \ln{\left ( e^{m x} + e^{- m x} \right )} h(x)=ln(emx+e−mx) হলে h′(0)= h^{'} \left ( 0 \right ) = h′(0)= কত ?
0
m
h(x)=ln(emx+e−mx) h(x)=\ln \left(e^{m x}+e^{-m x}\right) h(x)=ln(emx+e−mx)
∴h′(x)=1emx+e−mx⋅(meemx−me−mx)∴h′(0)=mem.0−me−m⋅0em⋅0+e−m⋅0=m−m1+1=02=0 \begin{array}{l} \therefore \mathrm{h}^{\prime}(\mathrm{x})=\frac{1}{\mathrm{e}^{\mathrm{mx}}+\mathrm{e}^{-\mathrm{mx}}} \cdot\left(\mathrm{me} \mathrm{e}^{\mathrm{mx}}-\mathrm{me}^{-\mathrm{mx}}\right) \\ \therefore \mathrm{h}^{\prime}(0)=\frac{\mathrm{me}^{\mathrm{m} .0}-\mathrm{me}^{-\mathrm{m} \cdot 0}}{\mathrm{e}^{\mathrm{m} \cdot 0}+\mathrm{e}^{-\mathrm{m} \cdot 0}}=\frac{\mathrm{m}-\mathrm{m}}{1+1}=\frac{0}{2}=0 \end{array} ∴h′(x)=emx+e−mx1⋅(meemx−me−mx)∴h′(0)=em⋅0+e−m⋅0mem.0−me−m⋅0=1+1m−m=20=0
ddx(1+sin2xsinx+cosx)=? \frac{d}{d x}\left(\frac{\sqrt{1+\sin 2 x}}{\sin x+\cos x}\right)=? dxd(sinx+cosx1+sin2x)=?
x এর মান কত হলে xlnx\mathrm{\frac{x}{lnx}}lnxx এর মান ক্ষুদ্রতম হবে?
If f(x)=e4x1+2exthan f′(0) is−f(x) = \frac{{{e ^{4x}}}}{{1 + 2{e ^x}}} than\,\,f'\left( 0 \right)\,\,is-f(x)=1+2exe4xthanf′(0)is−
If y=esin2x+sin4x+sin6x+....+∞y=e^{\sin^{2}x +\sin^{4}x + \sin ^{6}x +....+\infty} y=esin2x+sin4x+sin6x+....+∞ , then dydx=?\dfrac {dy}{dx} =?dxdy=?
