derivative x

Let f(x) = sin x. Then, we have ..

Let f(x) = sec x. Then, we have Similarly, we can prove tha..

..

So far we have discussed the derivative of a function f(x) at a point 'a' which is in the domain of f. Suppose we want to find the derivative of the same function at a different point 'b', then we have to compute the derivative by repeating the same process. ..

Quantity Formula Symbol (SI Unit) Area A=LxB m 2 Volume V=LxBXH m 3 Density D = Mass/Volume kg m - 3 Velocity V = Distance/Time m s -1 Acceleration a = Change in Velocity/Time m -2 Momentum p = mass x velocity Kg ms -1 F..

Let y = tan - 1 x. Then tan y = x. Differentiating both sides w.r.t. x, we get ..

Let y = sin - 1 x, then sin y = x. ..

Differentiating both sides with respect to x, we get Hence, we have..

The differentiation of function of a function is known as 'chain rule'. The chain rule is probably the most widely used differentiation rule in mathematics. If y is a differentiable function of u and u is a differentiable function of x, then the derivative of y with ..

as x approaches a through values less than 'a' is called Left hand derivative at x=a denoted by Lf '(a)...