Differentiation...

How many integers are there such that $$2 \le n \le 100$$ and the highest common factor of $$n$$ and $$36$$ is $$1$$?

If area of a triangle is $$35$$ square units with vertices $$\left( {2, - 6} \right),\,\,\left( {5,\,\,4} \right)$$ and $$({k},\,\,4)$$ then $${k}$$ is :

The number of ways in which $$9$$ persons can be divided into three equal groups, is

What is the next number in the series $$2,12,36,80,150?$$

Let $$f:[0,2]\rightarrow R$$ be a twice differentiable function such that $$f"(x)>0$$, for all $$x\in (0,2)$$ If $$\phi (x)=f(x)+f(2-x)$$, then $$\phi$$is:

The number of permutations which can be formed out of the letters of the word "SERIES" three letters together, is:

The coefficient of $$x^{18}$$ in the expansion of $$(1+x)(1-x)^{10}\{(1+x+x^2)^9\}$$ is?

Differentiate the following function with respect to x.
$$\dfrac{x^3}{3}-2\sqrt{x}+\dfrac{5}{x^2}$$.

Differentiate the following function with respect to x.
$$3^x+x^3+3^3$$.

 Let $$ u(x) $$ and $$ v(x) $$ be differentiable functions such that $$ \dfrac{u(x)}{v(x)}=7 . $$ If $$ \dfrac{u^{\prime}(x)}{v^{\prime}(x)}=p $$ and $$ \left(\dfrac{u(x)}{v(x)}\right)^{\prime}=q, $$ then $$ \dfrac{p+q}{p-q} $$ has the value equal to