গুণফল ,ভাগফল ও সংযোজিত ফাংশনের অন্তরজ/Chain Rule
xxx এর সাপেক্ষে অন্তরক সহগ নিচের কোনটি? ln{ex(x−1x+1)3/2} \ln \left\{e^{x}\left(\frac{x-1}{x+1}\right)^{3 / 2}\right\} ln{ex(x+1x−1)3/2}
x4+4x2−3 \frac{x^{4}+4}{x^{2}-3}x2−3x4+4
x2+2x2+1 \frac{x^{2}+2}{x^{2}+1}x2+1x2+2
x2−2x2−1 \frac{x^{2}-2}{x^{2}-1}x2−1x2−2
x2+2x2−1 \frac{x^{2}+2}{x^{2}-1}x2−1x2+2
Solve: Let y=ln{ex(x−1x+1)3/2} \mathrm{y}=\ln \left\{e^{x}\left(\frac{x-1}{x+1}\right)^{3 / 2}\right\} y=ln{ex(x+1x−1)3/2}
=lnex+32{ln(x−1)−ln(x+1)=x+32{ln(x−1)−ln(x+1)} \begin{array}{l} =\ln e^{x}+\frac{3}{2}\{\ln (x-1)-\ln (x+1)\\ =x+\frac{3}{2}\{\ln (x-1)-\ln (x+1)\} \end{array} =lnex+23{ln(x−1)−ln(x+1)=x+23{ln(x−1)−ln(x+1)}
∴dydx=1+32{1x−1−1x+1}=1+32{x+1−x+1(x−1)(x+1)}=1+32{2x2−1}=x2−1+3x2−1=x2+2x2−1( Ans. ) \begin{aligned} \therefore \quad \frac{d y}{d x} & =1+\frac{3}{2}\left\{\frac{1}{x-1}-\frac{1}{x+1}\right\} \\ & =1+\frac{3}{2}\left\{\frac{x+1-x+1}{(x-1)(x+1)}\right\} \\ & =1+\frac{3}{2}\left\{\frac{2}{x^{2}-1}\right\}=\frac{x^{2}-1+3}{x^{2}-1} \\ & =\frac{x^{2}+2}{x^{2}-1}(\text { Ans. }) \end{aligned} ∴dxdy=1+23{x−11−x+11}=1+23{(x−1)(x+1)x+1−x+1}=1+23{x2−12}=x2−1x2−1+3=x2−1x2+2( Ans. )
If the angle between the curves y=2x y = 2^x y=2x and y=3x y=3^x y=3x is α, \alpha, α, then the value of tanα \tan \alpha tanα is equal to :
Differentiate the following w.rd/dxd/dxd/dx
sinx logx\sin x\ log xsinx logx.
ddx(e2x−3)= \frac{d}{d x}\left(e^{\sqrt{2 x}-3}\right)= dxd(e2x−3)= কত?
If x=acos3θx = a \cos^3 \thetax=acos3θ and y=asin3θy = a\sin^3 \thetay=asin3θ, then 1+(dydx)21 + \left( \dfrac{dy}{dx} \right )^21+(dxdy)2 is
