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# Derivative Calculator

Enter the function and variable to find the derivative using 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

**The function**

*x*_{0}.**is said to be differentiable at**

*f(x)***and the derivative of**

*x*_{0},**at**

*f(x)***is given by:**

*x*_{0}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/x**^{2}*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 [x^{a}] = a * x^{a-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)] |

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) = sec ^{2}(x) = 1 + tan^{2}(x) |

Derivative of e^x (Exponential) | d/dx e^x = e^x |

Logarithm Derivatives | d/dx a^x = a |

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 | 3^{x} * ln(3) |

derivative of x^2 | 2x |

derivative of x^1/2 | 1/x^{1/2} |

derivative of 5^x | 5^{x} * ln(5) |

derivative of x/2 | 1/2 |

derivative of x^e | e * x^{e-1} |

derivative of 1/x | -1/x^{2} |

derivative of 2x | 2 |

derivative of 2 | 0 |

derivative of x^x | x^{x}(ln(x) + 1) |

derivative of x^-1 | -x^{-2} |

derivative of 2^x | 2^{x} * ln(2) |

derivative of 4^x | 4^{x} * 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.