If $y=x^{x^2}$ then $\frac{dy}{dx}=$

Important Questions on Differential Coefficient

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Beta Question Bank for Engineering: Mathematics>Chapter 28 - Differential Coefficient>EXERCISE-1>Q 19

If $x^m·y^n=(x+y{)}^{m+n}$, then $\frac{dy}{dx}$ is -

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Beta Question Bank for Engineering: Mathematics>Chapter 28 - Differential Coefficient>EXERCISE-1>Q 20

If $x\sqrt{(1+y)}+y\sqrt{(1+x)}=0$, then $\frac{dy}{dx}$ equals -

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Beta Question Bank for Engineering: Mathematics>Chapter 28 - Differential Coefficient>EXERCISE-1>Q 21

If $x^2{e}^y+2xy{e}^x+13=0$, then $\frac{dy}{dx}$ equals -

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Beta Question Bank for Engineering: Mathematics>Chapter 28 - Differential Coefficient>EXERCISE-1>Q 22

If $x=e^{y+e^{y+\cdots \mathrm{to} \infty }},x>0$ then $\frac{dy}{dx}$ is -

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Beta Question Bank for Engineering: Mathematics>Chapter 28 - Differential Coefficient>EXERCISE-1>Q 23

If $x=\theta -\frac{1}{\theta }$ and $y=\theta +\frac{1}{\theta }$, then $\frac{dy}{dx}=$

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Beta Question Bank for Engineering: Mathematics>Chapter 28 - Differential Coefficient>EXERCISE-1>Q 24

The derivative of ${\sin }^{-1}\left(\frac{x}{\sqrt{1+x^2}}\right)$ w.r.t. ${\cos }^{-1}\left(\frac{1-x^2}{1+x^2}\right),(x>0)$ is

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Beta Question Bank for Engineering: Mathematics>Chapter 28 - Differential Coefficient>EXERCISE-1>Q 25

Let $g$ is the inverse function of $f\&f^{\text{'}}\left(x\right)=\frac{x^{10}}{\left(1+x^2\right)}$. If $g\left(2\right)=a$ then $g^{\text{'}}\left(2\right)$ is equal to -

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Beta Question Bank for Engineering: Mathematics>Chapter 28 - Differential Coefficient>EXERCISE-1>Q 26

Let $f\left(x\right)=\sin x ; g\left(x\right)=x^2 \text{and} h\left(x\right)={\log }_{e}x \text{and} F\left(x\right)=h\left[g\left(f\left(x\right)\right)\right]$ then $\frac{d^{2}F}{d{x}^2}$ is equal to -