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 $x=\frac{5\pi }{4}$

A particle starts from rest and its angular displacement (in radians) is given by $\theta =\frac{t^2}{20}+\frac{t}{5}.$ If the angular velocity at the end of $t=4$ is $k,$ then the value of $5k$ is

If $a$ and $b$ are fixed non-zero constants, then the derivative of $\frac{a}{x^4}-\frac{b}{x^2}+\cos x$ is $ma+nb-p$ where

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

Let $f\left(x\right)=x-\frac{1}{x}$, then $f^{\text{'}}\left(–1\right)$ is