Differentiation is a method in Calculus which gives us the rate of change of the function value with respect to the change in the
variable of the function. Differentiation is a very important section in Calculus and Differentiation calculator is the quick online
tool which makes the calculations based on differentiation, easy and simple!
Example 1: Give the differentiation of the function, f(x) = x4 + lnx
To differentiate the above given function, we write it as
df(x)/dx = d(x4)/dx + d(ln x)/dx
Power rule of the Derivatives d f(xn)/dx = n*xn-1
Applying the above formula to the term x4, we get
d f(x)/dx = 4 * x4-1 + d (ln x)/dx
The derivative of ‘ln x’ expression is ‘1/x’
Hence the differentiation of the given function gives 4x3 + 1/x
Example 2: Give the differentiation of the function, f(x) = sin(x) + cos(x)
To differentiate the above given function, we write it as
d f(x)/dx = d sin(x)/dx + d cos(x)/dx
Here we have to find the derivatives of the trigonometric functions.
Derivative of sin(x) = cos(x)
Derivative of cos(x) = -sin(x)
Hence d f(x)/dx = cos(x) – sin(x)
The differentiation of the given function d f(x)/dx = cos(x) – sin(x)