Differentiation

If $y=\sec^{-1}\left(\frac{x+1}{x-1}\right)+\sin^{-1}\left(\frac{x-1}{x+1}\right)$, $x\in[0,\infty)$ and $x\ne1$, then $\dfrac{dy}{dx}$ is equal to

If $ f(x)=\displaystyle \int_{0}^{x} t\sin t, dt $, then $f'(x)$ is

Find $ \displaystyle \frac{d}{dx}\left( \sqrt{x} - \frac{5}{\sqrt{x}} \right) $

If x = a cos t, y = b sin t, then $\frac{d^{2}y}{dx^{2}}$ is

The minimum value of the function $y=2x^{3}+36x-20$ is

Find the point at which, the tangent to the curve $y=\sqrt{4x-3}-1$ as its slope $\frac{2}{3}$

Let $f(x)$ be a polynomial function of second degree and $f(1) = f(–1)$. If $a, b, c$ are in A.P. then $f'(a), f'(b), f'(c)$ are in.

If $f(x)=tan^{-1}\left [ \frac{sinx}{1+cosx} \right ]$ , then what is the first derivative of $f(x)$?

A function $f : (0,\pi) \to R$ defined by $f(x) = 2 sin x + cos 2x$ has

With the usual notation $\frac{d^{2}x}{dy^{2}}$

The equation of the tangent at any point of the curve $x=acos2t$, $y=2\sqrt{2}a sint$ with $m$ as its slope is

Differentiate [- log(log x),  x > 1] with respect to x

The derivative of (x³ + e^x + 3^x + cotx) with respect to x is

If y = cos² x² , find dy/dx