Find the derivative of the following function: $5 \sec x + 4 \cos x$.

If $f(x) = \frac{1+\sec x}{2(\sec x-1)}$ for $0 < x < \frac{\pi}{2}$ and $f^{\prime}(x) = f(x) \cdot g(x)$, then $g(x) =$

$A$ 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 $t = 4 \ s$ is $k$,then the value of $5k$ is

Let $f: R \rightarrow R$ be a function such that $f(x)=x^3+x^2 f^{\prime}(1)+x f^{\prime \prime}(2)+6, x \in R$,then $f(2)$ equals

$x = \frac{1-\sqrt{y}}{1+\sqrt{y}} \Rightarrow \frac{dy}{dx}$ is equal to

Differentiate $(x^{2}-5x+8)(x^{3}+7x+9)$ using the product rule.