The geometrical meaning of derivation is to give the slope of a tangent drawn at a particular point
. The method to arrive at this solution is, we need to know all the formulae to differentiate any given function. First of all differentiate a given function by applying the basic formula. Then apply the value of the given point in the resultant differentiated expression to get the slope of the tangent drawn on the curve at that given point. Let us note few formulae which we are going to apply.
1) 'd/(dx )(x^n) = nx^(n-1)'
2) 'd/(dx) (1/x) = -1/(x^2)'
3) 'd/(dx) (sqrt x ) = 1/(2 sqrt(x))'
4) 'd/(dx) (sinx)' = cos x
5) 'd/dx (cos x)' = -sinx
6) 'd/(dx) (e^x)' = 'e^x'
Now let us see few problems on this topic derivative of a function at a point.
Example Problems on Derivative of a Function at a Point.
Ex 1: Find the derivative of the function f(x) = x^2+2x+6 at (1,9).
Soln: Given: f(x) = x^2+2x+6
Therefore f (x) = 2x +2
Therefore f (1) = 2 (1) + 2 = 4
Therefore The derivative of the function at (1,9).
Ex 2: Find the derivative of the function f(x) = 3x^2+sqrt x at (4,50)