# What is the derivative of a ln function?

## What is the derivative of a ln function?

The derivative of ln(x) is 1/x.

## How do you derive derivatives of trig functions?

We can get the derivatives of the other four trig functions by applying the quotient rule to sine and cosine. For instance, ddx(tan(x))=(sin(x)cos(x))′=cos(x)(sin(x))′−sin(x)(cos(x))′cos2(x)=cos2(x)+sin2(x)cos2(x)=1cos2(x)=sec2(x).

**What are the properties of natural logarithms?**

Natural logarithm rules and properties

Rule name | Rule |
---|---|

Product rule | ln(x ∙ y) = ln(x) + ln(y) |

Quotient rule | ln(x / y) = ln(x) – ln(y) |

Power rule | ln(x y) = y ∙ ln(x) |

ln derivative | f (x) = ln(x) ⇒ f ‘ (x) = 1 / x |

**What are properties of logarithms?**

Comparison of Exponent law and Logarithm law

Properties/Rules | Exponents | Logarithms |
---|---|---|

Product Rule | xp.xq = xp+q | loga(mn) = logam + logan |

Quotient Rule | xp/xq = xp-q | loga(m/n) = logam – logan |

Power Rule | (xp)q = xpq | logamn = n logam |

### What is the integral of ln?

Definite Integral of ln x The formula for the integral of ln x is given by, ∫ln x dx = xlnx – x + C, where C is the constant of integration.

### What is the derivative of ax?

Derivative Rules

Common Functions | Function | Derivative |
---|---|---|

ax | a | |

Square | x2 | 2x |

Square Root | √x | (½)x-½ |

Exponential | ex | ex |

**What are the derivatives of the 6 trig functions?**

What are the Derivatives of the 6 Trig Functions?

- Derivation of sin x: (sin x)’ = cos x.
- Derivative of cos x: (cos x)’ = -sin x.
- Derivative of tan x: (tan x)’ = sec2 x.
- Derivative of cot x: (cot x)’ = -cosec2 x.
- Derivative of sec x: (sec x)’ = sec x. tan x.
- Derivative of cosec x: (cosec x)’ = -cosec x. cot x.

**How do you find the derivative of a cosine function?**

The derivative of the cosine function is written as (cos x)’ = -sin x, that is, the derivative of cos x is -sin x.