গুণফল ,ভাগফল ও সংযোজিত ফাংশনের অন্তরজ/Chain Rule
xxx এর সাপেক্ষে অন্তরক সহগ নিচের কোনটি? ln(sinx2) \ln \left(\sin x^{2}\right) ln(sinx2)
2xcot6x2 2 x \cot6 x^{2}2xcot6x2
2xtan4x2 2 x \tan4x^{2}2xtan4x2
2xcotx2 2 x \cot x^{2}2xcotx2
4xcotx3 4x \cot x^{3}4xcotx3
Solve:
ddx{ln(sinx2)}=1sinx2ddx(sinx2)=1sinx2(cosx2)ddx(x2)=2xcotx2 \begin{array}{l} \frac{d}{d x}\left\{\ln \left(\sin x^{2}\right)\right\}=\frac{1}{\sin x^{2}} \frac{d}{d x}\left(\sin x^{2}\right) \\ =\frac{1}{\sin x^{2}}\left(\cos x^{2}\right) \frac{d}{d x}\left(x^{2}\right)=2 x \cot x^{2} \end{array} dxd{ln(sinx2)}=sinx21dxd(sinx2)=sinx21(cosx2)dxd(x2)=2xcotx2
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