Derivatives of Polynomials and Trigonometric Functions

Find $\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2}$, if $\sqrt{\mathrm{x}+\mathrm{y}}+\sqrt{\mathrm{y}-\mathrm{x}}=\mathrm{c}$.

$\frac{\mathrm{d}}{\mathrm{dx}}\left\{{\tan }^{-1}(\sec x+\tan x)\right\}= ?$

If $f\left(x\right)=-\sqrt{25-x^2}$, then find the value of $\underset{x\to 1}{\lim }\frac{f\left(x\right)-f\left(1\right)}{x-1}$

If $f\left(x\right)$ is a polynomial such that $f\left(x+1\right)=f\left(x\right)+2x \forall x\in R$ and $f\left(0\right)=1$ then $f^{\text{'}}\left(5\right)=$

The differentiation of  $y=7x^4$ w.r.t. $x$ is

Find the derivative of the following function with respect to corresponding independent variable:

$y=10x^2+3$

Find the derivative of the following function with respect to the corresponding independent variables:

$f\left(x\right)=x+4\sin x$

The ${\left(n+1\right)}^{\mathrm{th}}$differentiation of an $n^{\mathrm{th}}$ order polynomial is

If $\sqrt{x}+\sqrt{y}=4$, then $\frac{dx}{dy}$ at $y=1$ is

Derivative of $x^{12}$ is 

Derivative of $x^{10}$ is 

If $y=\sqrt{x+\sqrt{x+\sqrt{x+\cdots \cdots \infty }}},$ then $\frac{dy}{dx}=$

If $y=c{\mathrm{os}}^{-1}\left(\cos x\right)$, then find $\frac{dy}{dx}$ at $x=\frac{5\pi }{4}$

Find $f^{\text{'}}\left(x\right)$ for the following:

$f\left(x\right)=3x^5$

Find $f^{\text{'}}\left(x\right)$ for the following:

$f\left(x\right)=2x^4$

If $f\left(x\right)=\left|x-2\right|+\left|x+1\right|-x$, then $f^{\text{'}}(-10)$ is equal to

If $ax+b{y}^2=\cos y$ then find $\frac{dy}{dx}$.

Let us let $f\left(t\right)\mathit{=}{t}^{\mathit{2}}$ for the interval  $0\le t\le 1$ and $g\left(t\right)\mathit{=}{t}^{\mathit{3}}$ for the interval  $0\le t\le 1.$ The value of $\mathrm{c}$ with $0<c<1$ at which $\frac{f\left(1\right)-f\left(0\right)}{g\left(1\right)-g\left(0\right)}=\frac{f^{\mathit{\text{'}}}\left(c\right)}{g^{\mathit{\text{'}}}\left(c\right)},$ is
 

If $f\left(x\right)$ is a linear function of $x$ such that $f^{\text{'}}\left(1\right)=5$  and $f\left(0\right)=0,$then $\sum _{x=1}^{n}f\left(x\right)$ is

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 $f^{\prime }\left(0\right)=$