গুণফল ,ভাগফল ও সংযোজিত ফাংশনের অন্তরজ/Chain Rule
xxx এর সাপেক্ষে অন্তরক সহগ নিচের কোনটি? ln(sin2x) \ln (\sin 2 x) ln(sin2x)
2cot2x 2 \cot 2 x2cot2x
4cot6x 4 \cot 6 x4cot6x
2tan2x 2 \tan 2 x2tan2x
2cot4x 2 \cot 4 x2cot4x
Solve:
ddx{ln(sin2x)}=1sin2xddx(sin2x)=1sin2x(cos2x)ddx(2x)=2cot2x \begin{array}{l} \frac{d}{d x}\{\ln (\sin 2 x)\}=\frac{1}{\sin 2 x} \frac{d}{d x}(\sin 2 x) \\ =\frac{1}{\sin 2 x}(\cos 2 x) \frac{d}{d x}(2 x)=2 \cot 2 x \end{array} dxd{ln(sin2x)}=sin2x1dxd(sin2x)=sin2x1(cos2x)dxd(2x)=2cot2x
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