গুণফল ,ভাগফল ও সংযোজিত ফাংশনের অন্তরজ/Chain Rule
ddx(e2x−3)= \frac{d}{d x}\left(e^{\sqrt{2 x}-3}\right)= dxd(e2x−3)= কত?
2(e2x−3) \sqrt{2}\left(e^{\sqrt{2 x} - 3}\right) 2(e2x−3)
(e2x−3)2 \frac{\left(e^{\sqrt{2 x} - 3}\right)}{\sqrt{2}} 2(e2x−3)
(e2x−3)2x \frac{\left(e^{\sqrt{2 x} - 3}\right)}{\sqrt{2 x}} 2x(e2x−3)
2(e2x−3)x \frac{\sqrt{2} \left(e^{\sqrt{2 x} - 3}\right)}{\sqrt{x}} x2(e2x−3)
ddx[e2x−3]=e2x−3⋅ddx[2x−3]=e2x−3⋅(2⋅ddx[x]+ddx[−3])=e2x−3⋅(2⋅12x12−1+0)=e2x−32x \begin{array}{c}\frac{\mathrm{d}}{\mathrm{d} x}\left[\mathrm{e}^{\sqrt{2} \sqrt{x}-3}\right] \\ =\mathrm{e}^{\sqrt{2} \sqrt{x}-3} \cdot \frac{\mathrm{d}}{\mathrm{d} x}[\sqrt{2} \sqrt{x}-3] \\ =\mathrm{e}^{\sqrt{2} \sqrt{x}-3} \cdot\left(\sqrt{2} \cdot \frac{\mathrm{d}}{\mathrm{d} x}[\sqrt{x}]+\frac{\mathrm{d}}{\mathrm{d} x}[-3]\right) \\ =\mathrm{e}^{\sqrt{2} \sqrt{x}-3} \cdot\left(\sqrt{2} \cdot \frac{1}{2} x^{\frac{1}{2}-1}+0\right) \\ =\frac{\mathrm{e}^{\sqrt{2} \sqrt{x}-3}}{\sqrt{2} \sqrt{x}}\end{array} dxd[e2x−3]=e2x−3⋅dxd[2x−3]=e2x−3⋅(2⋅dxd[x]+dxd[−3])=e2x−3⋅(2⋅21x21−1+0)=2xe2x−3
cosx \cos{\sqrt{x}} cosx এর অন্তরক সহগ কোনটি?
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 প্রেক্ষিতে ln(1 + ex) এর অন্তরজ কোনটি?
x এর মান কত হলে xlnx\mathrm{\frac{x}{lnx}}lnxx এর মান ক্ষুদ্রতম হবে?
