Find $\frac{d^{2}y}{d{x}^2}$, if $y$ is equal to $x^3+5x^2-3x+10$.

Important Questions on Differential Coefficient

EASY

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

If ${\mathrm{e}}^y(x+1)=1$, then $\frac{d^{2}y}{d{x}^2}=$

HARD

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

If $y=e^{nx}$, then $\frac{d^{2}y}{d{x}^2}.\frac{d^{2}x}{d{y}^2}$  is equal to :

HARD

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

If $y^2+{\log }_e\left({\cos }^{2}x\right)=y, x\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$ then :

EASY

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

If $y=2x^{n+1}+\frac{3}{x^n}$, then $x^2\frac{{\mathrm{d}}^{2}y}{\mathrm{d}{x}^2}$ is

EASY

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

If $x=A\cos 4t+B\sin 4t$$,$ then $\frac{d^{2}x}{d{t}^2}=$

HARD

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

If $a{x}^2+2hxy+b{y}^2=0,$ then $\frac{d^{2}y}{d{x}^2}=$

EASY

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

If $x=a {\sec }^2\theta ,y=a {\tan }^2\theta$ then $\frac{d^{2}y}{d{x}^2}=$

HARD

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

If $x=\log t, y+1=\frac{1}{t}$, then $e^{-x}\frac{d^{2}x}{d{y}^2}+\frac{dx}{dy}=$

MEDIUM

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

If $y={\left[x+\sqrt{x^2-1}\right]}^{15}+{\left[x-\sqrt{x^2-1}\right]}^{15}$, then $\left(x^2-1\right)\frac{d^{2}y}{d{x}^2}+x\frac{dy}{dx}$ is equal to

HARD

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

If $2x=y^{\frac{1}{5}}+y^{-\frac{1}{5}}$ and $\left(x^2-1\right)\frac{d^{2}y}{d{x}^2}+\lambda x\frac{dy}{dx}+ky=0$, then $\lambda +k$ is equal to

MEDIUM

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

If $y=\frac{{\left({\sin }^{-1}x\right)}^2}{2}$, then $\left(1-x^2\right)y_2-x{y}_1=$

HARD

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

If ${\cos }^{-1}\left(\frac{y}{b}\right)=\log \left(\frac{x}{n}\right),$ then $x^2{y}_2+x{y}_1=$

EASY

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

If $y=e^{4x}\cos 5x,$ then $\frac{d^{2}y}{d{x}^2}$ at $x=0$ is

HARD

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

If $x=e^{\mathit{t}}\sin t$ and $y=e^{\mathit{t}}\cos t$, $\mathrm{t}$ is a parameter, then the value of $\frac{d^{2}x}{d{y}^2}+\frac{d^{2}y}{d{x}^2}$ at $t=0,$ is

EASY

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

If $y=3e^{5x}+5e^{3x}$, then $\frac{d^{2}y}{d{x}^2}-8\frac{dy}{dx}=$

MEDIUM

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

Expansion of $\log \left(1+3x+2x^2\right)$ is

MEDIUM

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

If $y=a\sin x+(5+2x)\cos x,$ then $y^{\text{'}\text{'}}+y=$

MEDIUM

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

Let $C\left(\theta \right)= \sum _{n=0}^{\infty }\frac{\cos \left(n\theta \right)}{n !}$ Which of the following statements is FALSE?

MEDIUM

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

If $x+y={\tan }^{-1}y$ and $y^{″}=f\left(y\right)y^{\prime },$ then $f\left(y\right)=$

MEDIUM

Mathematics>Differential Calculus>Differential Coefficient>Higher Order Derivatives

If $x^2+y^2=1$, then