Differentiate w.r.t. x

(i) $x^{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

Important Questions on Differentiation

MEDIUM

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

If $f\left(x\right)=x^6+6^x,$ then $f^{\prime }\left(x\right)$ is equal to

MEDIUM

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

If $x=\sqrt{2^{{\mathrm{cosec}}^{-1}t}}$ and  $y=\sqrt{2^{{\sec }^{-1}t}}, \left(\left|t\right|\ge 1\right),$ then $\frac{dy}{dx}$ is equal to

MEDIUM

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

If $x=a\left(t-\frac{1}{t}\right), y=a\left(t+\frac{1}{t}\right)$ where $t$ be the parameter then $\frac{dy}{dx}=?$

HARD

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

Let $p\left(x\right)$ be a polynomial such that $p\left(x\right)-p^{\text{'}}\left(x\right)=x^n$ where $n$ is a positive integer. Then, $p\left(0\right)$ equals

EASY

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

If the function $f\left(x\right)$ defined by $f\left(x\right)=\frac{x^{100}}{100}+\frac{x^{99}}{99}+......+\frac{x^2}{2}+x+1,$ then $f^{\prime }\left(0\right)=$

HARD

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

Let $f$ be a polynomial function such that $f\left(3x\right)=f^{\prime }\left(x\right). f^{\prime \prime }\left(x\right),$ for all $x\in R.$ Then :

MEDIUM

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

If $x=f\left(t\right)$ and $y=g\left(t\right)$ are differentiable functions of $t$ then $\frac{d^{2}y}{d{x}^2}$ is

HARD

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

The derivative of ${\mathrm{t}\mathrm{a}\mathrm{n}}^{-1}\left(\frac{\mathrm{s}\mathrm{i}\mathrm{n}x-\mathrm{c}\mathrm{o}\mathrm{s}x}{\mathrm{s}\mathrm{i}\mathrm{n}x+\mathrm{c}\mathrm{o}\mathrm{s}x}\right)$ with respect to $\frac{x}{2},$ where $x\in \left(0,\frac{\pi }{2}\right)$, is

MEDIUM

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

If $y=x^{x^{x^{.....\infty }}},$ then $y^{\prime }$ is equal to

MEDIUM

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

If $y={\sin }^{-1}\frac{1}{2}\left(\sqrt{1+x}+\sqrt{1-x}\right)$ then $y^{\prime }$ is equal to

MEDIUM

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

If $g$ is the inverse of a function $f$ and $f^{\text{'}}\left(x\right)=\frac{1}{1+x^5},$ then $g^{\text{'}}\left(x\right)$ is equal to 

MEDIUM

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

If $y=\frac{x+c}{1+x^2}$ where $c$ is a constant, when $y$ is stationary, $xy$ is equal to -

HARD

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

If $f\left(x\right)=\left|\begin{array}{ccc}\cos 2x& \cos 2x& \sin 2x\\ -\cos x& \cos x& -\sin x\\ \sin x& \sin x& \cos x\end{array}\right|,$ then

MEDIUM

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

If $y=\frac{{\sin }^{2}x}{1+\cot x}+\frac{{\cos }^{2}x}{1+\tan x}$$,$ then $y^{\prime }\left(x\right)$ is equal to

EASY

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

If $f\left(1\right)=1,f^{\text{'}}\left(1\right)=3$, then the derivative of $f\left(f\left(f\left(x\right)\right)\right)+{\left(f\left(x\right)\right)}^2$ at $x=1$ is:

EASY

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

If then $\mathrm{}{x}^y=e^{x-y},$ then $\frac{dy}{dx}$ at $x=1$ is ….

EASY

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

If $e^y+xy=e,$ the ordered pair $\left(\frac{dy}{dx},\frac{d^{2}y}{d{x}^2}\right)$ at $x=0$ is equal to

MEDIUM

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

If $x^m{y}^n={\left(x+y\right)}^{m+n}$ then $y^{\prime }$ is equal to

MEDIUM

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

If $x=3 \mathrm{t}\mathrm{a}\mathrm{n}t$ and $y=3 \mathrm{s}\mathrm{e}\mathrm{c}t,$ then the value of $\frac{d^{2}y}{d{x}^2}$ at $t=\frac{\pi }{4},$ is:

EASY

Mathematics>Differential Calculus>Differentiation>Differentiation of x to the Power n

Let $f\left(-x\right)=f\left(x\right)$. Then $f^{\text{'}}\left(x\right)$ must be