পর্যায়ক্রমিক অন্তরজ (Successive Differentiation)
যদি y=(xx)x হয়, তবে dy/dx=?
x(1+2logx)
xx.2logx
(xx).(1+logx)
(xx)x.x(1+2logx)
y=(xx)x⇒y=xx2y=\left(x^x\right)^x\Rightarrow y=x^{x2}y=(xx)x⇒y=xx2
∴dydx=ddx(xx2)=xx2ddx(x2lnx)=xx2(x+2xlnx)\therefore\frac{dy}{dx}=\frac{d}{dx}\left(x^{x^2}\right)=x^{x^2}\frac{d}{dx}\left(x^2\ln x\right)=x^{x^2}\left(x+2x\ln x\right)∴dxdy=dxd(xx2)=xx2dxd(x2lnx)=xx2(x+2xlnx)
=xx2.x(1+2lnx)=(xx)x.x(1+2logx)=x^{x^2}.x\left(1+2\ln x\right)=\left(x^x\right)^x.x\left(1+2\log x\right)=xx2.x(1+2lnx)=(xx)x.x(1+2logx)
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=cos2x y=\sqrt{\cos 2 x} y=cos2x হলে, (yy1)2=? \left(y y_{1}\right)^{2}= ? (yy1)2=?
x=a(t+sint),y=a(1−cost) \mathrm{x}=\mathrm{a}(\mathrm{t}+\sin \mathrm{t}), \mathrm{y}=\mathrm{a}(1-\cos \mathrm{t}) x=a(t+sint),y=a(1−cost) হলে d2ydx2= \frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}= dx2d2y= ?
y=1x=x−1 y=\frac{1}{x}=x^{-1} y=x1=x−1 এর n n n তম অন্তরক সহগ নিচের কোনটি ?
