Differentiation...

The points $$A (2, 9), B (a, 5)$$ and $$C (5, 5) $$ are the vertices of a triangle $$ABC$$ right angled at $$B$$. Find the values of  $$a$$ and hence the area of $$\Delta $$ $$ABC$$.

The area of triangle ABC (in sq. units) is :

Given:   $$\dfrac {20!}{18!}=380$$

Area of the triangle formed by the points P(-1.5, 3), Q(6, -2) and R(-3, 4) is 0.

If $$y^x=x^y$$, then find $$\displaystyle\frac{dy}{dx}$$.

If $$y=x^{-\tfrac12}+\log_5x+\displaystyle \frac {\sin x}{\cos x}+2^x$$, then find $$\dfrac {dy}{dx}$$

$$\displaystyle\frac{dy}{dx}$$ for $$y=x^x$$ is

For the function $$f(x) = \displaystyle \frac{x^{100}}{100} + \frac{x^{99}}{99} + ........... + \frac{x^2}{2} + x+1$$, $$f'(1) =$$

If $$y=x^2+sin^{-1}x+log_ex$$, find $$\dfrac {dy}{dx}$$

A graph may be defined as a set of points connected by lines called edges. Every edge connects a pair of points. Thus, a triangle is a graph with 3 edges and 3 points. The degree of a point is the number of edges connected to it. For example, a triangle is agraph with three points of degree 2 each. Consider a graph with 12 points. It is possible to reach any point from any other point through a sequence of edges. The number of edges "e" in the graph must satisfy the condition