Derivative calculator (A.K.A differentiation calculator) is used to determine the rate of change of the given function with respect to its independent variable. The function can be constant, linear, polynomial, quadric polynomial, etc.

The differential calculator will recognize the function and calculate its derivative. There are three kinds of differential.

- Explicit differentiation
- Implicit differentiation
- Partial differentiation

This derivative solver evaluates the explicit differentiation of any function with just one click.

To solve the problems of explicit differentiation, follow the steps below.

- Enter the constant, linear, or polynomial function into the input box.
- Select the independent variable like x, y, z, u, v, t, or w.
- Use the
**keypad icon** - Write the number of derivatives e.g, 1 for the first derivative or 2 for the second derivative.
- Click the
**calculate**button below the input box to get the results. - Press the
**reset**button to enter another function. - You can click
**show more**to view the step-by-step solution.

The derivative is the rate of change of the function with respect to its variable. Derivatives are fundamental to the solution of problems in differential equations and calculus.

The inverse process of differentiation is known as integral.

Here are some basic rules of differentiation are mentioned below.

Names | Rules |

Constant rule | \(\frac{d}{dx}\left(c\right)=0\) |

Power rule | \(\frac{d}{dx}\left(u\right)^n=nu^{n-1}\) |

Sum rule | \(\frac{d}{dx}\left(u\left(x\right)+v\left(x\right)\right)=\frac{d}{dx}\left(u\left(x\right)\right)+\frac{d}{dx}\left(v\left(x\right)\right)\) |

Difference rule | \(\frac{d}{dx}\left(u\left(x\right)-v\left(x\right)\right)=\frac{d}{dx}\left(u\left(x\right)\right)-\frac{d}{dx}\left(v\left(x\right)\right)\) |

Product rule | \(\frac{d}{dx}\left(u\left(x\right)\cdot v\left(x\right)\right)=v\left(x\right)\frac{d}{dx}\left(u\left(x\right)\right)+u\left(x\right)\frac{d}{dx}\left(v\left(x\right)\right)\) |

Quotient rule | \(\frac{d}{dx}\left(\frac{u\left(x\right)}{v\left(x\right)}\right)=\frac{v\left(x\right)\frac{d}{dx}\left(u\left(x\right)\right)-u\left(x\right)\frac{d}{dx}\left(v\left(x\right)\right)}{\left(v\left(x\right)\right)^2}\) |

How to calculate derivatives?

Below are some examples solved by using our d/dx calculator.

**Example**

Calculate the derivative of \(x^2+3x\)

**Solution**

**Step 1:** Apply the derivative notation in the given expression.

\(\frac{d}{dx}\left(x^2+3x\right)\)

**Step 2:** To solve the above function, apply the sum and the power rule.

\(\frac{d}{dx}\left(x^2+3x\right)\) = \(\frac{d}{dx}\left(x^2\right)\) + \(\frac{d}{dx}\left(3x\right)\)

\(\frac{d}{dx}\left(x^2+3x\right)\)= \(2x^{2-1}+3x^{1-1}\)

\(\frac{d}{dx}\left(x^2+3x\right)\) = \(2x^1+3x^0\)

\(\frac{d}{dx}\left(x^2+3x\right)\) = \(2x+3\left(1\right)\)

\(\frac{d}{dx}\left(x^2+3x\right)\)= \(2x+3\)

Here are some well-known examples of differentiation solved by our differential calculator.

Question | Answer |

Derivative of e^x | e^x |

Derivative of 2 | 0 |

Derivative of x | 1 |

Derivative of 2^x | 2^x ln2 |

Derivative of 1/x | -1/x^2 |

Derivative of a^x | ln(a)a^x |

Derivative of ln(x) | 1/x |

Derivative of 2*1 | 0 |

Derivative of sinx | cosx |

Derivative of cosx | -sinx |

Derivative of tanx | sec^2x |

Derivative of secx | tanx secx |

Derivative of sin(3x) | 3cos3x |

Derivative of sin2x | 2cos2x |

Derivative of sin^2x | 2sinx cosx |

Derivative of cos^3x | -3sinx cos^2x |

Derivative of sin(3x+1) | 3cos(3x+1) |

Derivative of sin^4x | 4sin^3x cosx |

Derivative of cotx | -csc^2x |

Derivative of tan2x | 2sec^2(2x) |

Derivative of sec^2x | 2tanxsec^2x |

Derivative of 2x | 2 |

Derivative of 1/sqrt(x) | -1/2x^(3/2) |

Derivative of root x | ½ x^ (-1/2) |

Derivative of 1/e^x | -e^(-x) |

Derivative of 1/sinx | -cot(x)csc(x) |

Derivative of 1/cosx | tan(x)sec(x) |

Derivative of 1/(1+x^2) | -2x/(1+x^2)^2 |

- What is derivative? | Encyclopædia Britannica.
- Rules of differentiation. Study.com | Take Online Courses. Earn College Credit.

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