What is the derivative of Secant?

What is the derivative of Secant?

The derivative of sec x with respect to x is sec x · tan x. i.e., it is the product of sec x and tan x. We denote the derivative of sec x with respect to x with d/dx(sec x) (or) (sec x)’. Thus, d/dx (sec x) = sec x · tan x (or)

What is the derivative of log5x?

Calculus Examples The derivative of log5(x) log 5 ( x ) with respect to x is 1xln(5) 1 x ln ( 5 ) .

What is the derivative of a logarithmic function?

Sayani R. The derivative of a logarithmic function is (1/the function)*derivative of the function.

What is the exponential rule for derivatives?

The exponential rule is a special case of the chain rule. It is useful when finding the derivative of e raised to the power of a function. The exponential rule states that this derivative is e to the power of the function times the derivative of the function.

How do you differentiate sec 1x?

by dividing by secytany ,

  1. ⇒y’=1secytany.
  2. ⇒y’=1x√x2−1.
  3. ddx(sec−1x)=1x√x2−1.

What is the derivative of log 3?

Calculus Examples The derivative of log3(x) log 3 ( x ) with respect to x is 1xln(3) 1 x ln ( 3 ) .

What are the derivative formulas?

General Derivative Formulas:

  • ddx(c)=0 where c is any constant.
  • ddxxn=nxn–1 is called the Power Rule of Derivatives.
  • ddxx=1.
  • ddx[f(x)]n=n[f(x)]n–1ddxf(x) is the Power Rule for Functions.
  • ddx√x=12√x.
  • ddx√f(x)=12√f(x)ddxf(x)=12√f(x)f′(x)
  • ddxc⋅f(x)=cddxf(x)=c⋅f′(x)

What is the derivative of E E X?

The derivative of the exponential function with base e is equal to ex. The derivative of eax is aeax. Using this formula, we have the differentiation of ex to be 1.

How do you find the derivative of Secx 2?

Therefore, to find the derivative of sec 2 x, we take the following steps:

  1. Find the derivative of f(x) = x 2, which is f'(x) = 2x.
  2. Plug g(x) = sec x into f'(x) from step 1.
  3. Multiply the result of step 2 by the derivative of g(x) = sec x, which is g'(x) = secx tanx.

What is sec 1x?

sec x−1 = sec(x)−1 = exsec(x) or exsecant of x, an old trigonometric function. sec x−1, sometimes interpreted as (sec(x))−1 = 1sec(x) = cos(x) or cosine of x, the multiplicative inverse (or reciprocal) of the trigonometric function secant (see above for ambiguity)