Derivative or Differentiation is a very important method used in Calculus math. Finding the derivative of a function is finding the
rate at which a function value changes with respect to change in the variable of the function. Derivative calculator wolfram is an
instant online tool very helpful in finding the derivative of a function and its other details.
Example 1: Find the derivative of the function, f(x) = x3 – 4x
Power rule of the Derivatives d f(xn)/dx = n*xn-1
Given function: x3 – 4x
Applying the above formula for every term of the function, we get
Derivative of the given function d f(x)/dx= d (x3)/dx – 4*d(x)/dx
df(x)/dx = 3*x3-1 – 4
df(x)/dx = 3x2 – 4
Hence the derivative of the function f(x) = x3 – 4xis 3x2– 4
Example 2: Find the derivative of the function, f(x) = 2x2 + 5x – 1
Power rule of the Derivatives d f(xn)/dx = n*xn-1
Given function: 2x2 + 5x – 1
Applying the above formula for every term of the function, we get
Derivative of the given function d f(x)/dx= d (2x2)/dx + 5*d(x)/dx – d(1)/dx
df(x)/dx = 2*2x2-1 + 5x – 0 (Derivative of a constant is always ‘0’)
d f(x)/dx = 4x1+ 5
Hence the derivative of the function f(x) = 2x2 + 5x – 1is 4x + 5