Derivative Calculator

Differentiation Calculator

Differentiation calculator is an online calculus tool that finds the derivative of a given function. This derivative calculator can perform explicit differentiation with just one click.

Our differential calculator shows the solution with steps in a couple of seconds. 

Derivative – Definition

Let f(x) be a function whose domain contains an open interval at some point x₀. The function f(x) is said to be differentiable at x₀, and the derivative of f(x) at x₀ is given by:

In other words, derivative measures the sensitivity to change of the function value with respect to a change in its argument. The reverse function of derivative is known as antiderivative.

How to calculate derivative?

To differentiate a function, you can use d/dx calculator above. Let’s calculate the derivative of 1/x to grasp the basic idea of derivation.

As 1/x = x^-1

We will use product rule (refer to below rules).

d/dx (x^-1) = -1(x^-2) = - 1/x²

Example:

Find the derivative of (x+7)².

Solution:

Step 1: Apply derivation symbol.

Step 2: Apply power rule.

Some functions need second derivative to complete the process of differentiation. You can use our second derivative calculator in this case.

Derivative rules – Formulas

Rules Name	Rules
Constant Rule	d/dx [k] = 0
Power Rule	d/dx [xa] = a * xa-1
Sum Rule	[f(x) + g(x)]' = f'(x) + g'(x)
Difference Rule	[f(x) - g(x)]' = f'(x) - g'(x)
Product Rule	[f(x) * g(x)]' = f'(x) g(x) + g'(x) f(x)
Quotient Rule	[f(x) / g(x)]' = [f'(x) g(x) - g'(x) f(x)]/[g(x)]2
Chain Rule	If f(x) = hg(x) f'(x) = h'(g(x)) * g'(x)
Trigonometric Derivatives	d/dx cos(x) = -sin(x) d/dx sin(x) = cos(x) d/dx tan(x) = sec2(x) = 1 + tan2(x)
Derivative of e^x (Exponential)	d/dx e^x = e^x
Logarithm Derivatives	d/dx a^x = ax ln(a), a>0 d/dx ln(x) = 1/x, x>0 d/dx logx(x) = 1/(x ln(a)), x>0

Use our derivative calculator with steps to differentiate the functions according to the above rules of differentiation. Here are some examples of deriavtive solved by our differentiate calculator.

Function	Derivative of the function
derivative of x	1
derivative of 3^x	3x * ln(3)
derivative of x^2	2x
derivative of x^1/2	1/x1/2
derivative of 5^x	5x * ln(5)
derivative of x/2	1/2
derivative of x^e	e * xe-1
derivative of 1/x	-1/x2
derivative of 2x	2
derivative of 2	0
derivative of x^x	xx(ln(x) + 1)
derivative of x^-1	-x-2
derivative of 2^x	2x * ln(2)
derivative of 4^x	4x * ln(4)

You can cross check the above resut by using our derivative calculator.

Referrences

• Khan Academy. (n.d.). Derivative – Definition. Khan Academy
• Wikimedia Foundation. (2022, August 28). Differentiation rules. Wikipedia.