পর্যায়ক্রমিক অন্তরজ (Successive Differentiation)
xxx এর সাপেক্ষে অন্তরক সহগ নিচের কোনটি? tan−1a+bxb−ax \tan ^{-1} \frac{a+b x}{b-a x} tan−1b−axa+bx
0
11−x2 \frac{1}{1-x^{2}} 1−x21
11+x2 \frac{1}{1+x^{2}} 1+x21
1
Solve:
=tan−1b(ab+x)b(1−abx)=tan−1(ab)+tan−1(x)∴ddx{tan−1a+bxb−ax}=ddx{tan−1(ab)}+ddx{tan−1(x)} \begin{array}{c} =\tan ^{-1} \frac{b\left(\frac{a}{b}+x\right)}{b\left(1-\frac{a}{b} x\right)}=\tan ^{-1}\left(\frac{a}{b}\right)+\tan ^{-1}(x) \\ \therefore \quad \frac{d}{d x}\left\{\tan ^{-1} \frac{a+b x}{b-a x}\right\}=\frac{d}{d x}\left\{\tan ^{-1}\left(\frac{a}{b}\right)\right\}+ \\ \frac{d}{d x}\left\{\tan ^{-1}(x)\right\} \end{array} =tan−1b(1−bax)b(ba+x)=tan−1(ba)+tan−1(x)∴dxd{tan−1b−axa+bx}=dxd{tan−1(ba)}+dxd{tan−1(x)}
=0+11+x2=11+x2 =0+\frac{1}{1+x^{2}}=\frac{1}{1+x^{2}} =0+1+x21=1+x21
f(x)=lnx,g(x)=(x+1+x2)f(x)=\ln x, g(x)=\left(x+\sqrt{1+x^{2}}\right)f(x)=lnx,g(x)=(x+1+x2)
y=ex y=e^{x} y=ex হলে, y4 \mathrm{y}_{4} y4 কত ?
y=lnex2 y=\operatorname{ln} e^{x^{2}} y=lnex2 হলে y2=? y_{2}=? y2=?
y=1x3 y=\frac{1}{x^{3}} y=x31 বক্ররেখার (−1,−1) (-1,-1) (−1,−1) বিন্দুতে y1 \mathrm{y}_{1} y1 এর মান কোনটি?
