If y(x)=xx, x0, then y prime prime(2)-2 y prime(2) is equal to :

Question

If y(x)=xx, x>0, then y prime prime(2)-2 y prime(2) is equal to : (A) 4( log e 2)2-2 (B) 8 log e 2-2 (C) 4( log e 2)2+2 (D) 4 log e 2+2

Tardigrade Admin · Accepted Answer

y prime=xx y prime=xx(1+ℓ n x) y prime prime=xx(1+ℓ n x)2+xx ⋅ (1/x) y prime prime(2)=4(1+ℓ operatornamen 2)2+2 y prime(2)=4(1+ℓ n 2) y prime prime(2)-2 y prime(2)=4(1+ℓ operatornamen 2)2+2-8(1+ℓ n 2) =4(1+ℓ n 2)[1+ℓ n 2-2]+2 .=4(ℓ n 2)2-1)+2 =4(ℓ n 2)2-2

Q. If $y (x) = x^{x}, x > 0$ , then $y^{''} (2) - 2 y^{'} (2)$ is equal to :

$4 (lo g_{e} 2)^{2} - 2$

$8 lo g_{e} 2 - 2$

$4 (lo g_{e} 2)^{2} + 2$

$4 lo g_{e} 2 + 2$

Q. If y(x)=xx,x>0, then y′′(2)−2y′(2) is equal to :

4(loge​2)2−2

8loge​2−2

4(loge​2)2+2

4loge​2+2

y′=xx y′=xx(1+ℓnx) y′′=xx(1+ℓnx)2+xx⋅x1​ y′′(2)=4(1+ℓn2)2+2 y′(2)=4(1+ℓn2) y′′(2)−2y′(2)=4(1+ℓn2)2+2−8(1+ℓn2) =4(1+ℓn2)[1+ℓn2−2]+2 =4(ℓn2)2−1)+2 =4(ℓn2)2−2

Q. If $y (x) = x^{x}, x > 0$ , then $y^{''} (2) - 2 y^{'} (2)$ is equal to :

$4 (lo g_{e} 2)^{2} - 2$

$8 lo g_{e} 2 - 2$

$4 (lo g_{e} 2)^{2} + 2$

$4 lo g_{e} 2 + 2$