অব্যক্ত ফাংশন (Implicit Function)
অন্তরিকরণ কর : ddx(5x2−4)3 \frac{d}{dx} \sqrt[3]{\left ( 5 x^{2} - 4 \right )} dxd3(5x2−4)
x3(5x2−4)3+c \frac{x}{3 \sqrt[3]{\left ( 5 x^{2} - 4 \right )}} + c 33(5x2−4)x+c
10x3(5x2−4)23+c \frac{10 x}{3 \sqrt[3]{\left ( 5 x^{2} - 4 \right )^{2}}} + c 33(5x2−4)210x+c
10x(5x2−4)23+c \frac{10 x}{\sqrt[3]{\left ( 5 x^{2} - 4 \right )^{2}}} + c 3(5x2−4)210x+c
None of these
ddx(5x2−43)=ddx[(5x2−4)13]=13(5x2−4)−23⋅10x=10x3(5x2−4)23 \frac{\mathrm{d}}{\mathrm{dx}}\left(\sqrt[3]{5 \mathrm{x}^{2}-4}\right)=\frac{\mathrm{d}}{\mathrm{dx}}\left[\left(5 \mathrm{x}^{2}-4\right)^{\frac{1}{3}}\right]=\frac{1}{3}\left(5 \mathrm{x}^{2}-4\right)^{-\frac{2}{3}} \cdot 10 \mathrm{x}=\frac{10 \mathrm{x}}{3 \sqrt[3]{\left(5 \mathrm{x}^{2}-4\right)^{2}}} dxd(35x2−4)=dxd[(5x2−4)31]=31(5x2−4)−32⋅10x=33(5x2−4)210x
যদি y=sin3xcos2x তবে yn এর মান নীচের কোনটি?
f(x)=cosx f(x)=\cos x f(x)=cosx এবং g(x)=x1+y+y1+x g(x)=x \sqrt{1+y}+y \sqrt{1+x} g(x)=x1+y+y1+x যেখানে x≠y x \neq y x=y
(i) ey={e3x(3x−13x+1)52} \mathrm{e}^{\mathrm{y}}=\left\{\mathrm{e}^{3 x}\left(\frac{3 \mathrm{x}-1}{3 \mathrm{x}+1}\right)^{\frac{5}{2}}\right\} ey={e3x(3x+13x−1)25},(ii) y=sin3x y=\sin 3 x y=sin3x