Question

what is the derivative of log tanx base e​

Answer 1

Answer:

logae=lnelna=1lna. Thus, y′(x)=(logax)′=1xlna. If a=e, we obtain the natural logarithm the derivative of which is expressed by the formula (lnx)′=1x.

Step-by-step explanation:

Derivatives of Basic Trigonometric Functions

Using the quotient rule it is easy to obtain an expression for the derivative of tangent: (tanx)′=(sinxcosx)′=(sinx)′cosx−sinx(cosx)′cos2x=cosx⋅cosx−sinx⋅(−sinx)cos2x=cos2x+sin2xcos2x=1cos2x. The derivative of cotangent can be found in the same way.

hope you got correct✅✔ answer

Answer 2

Answer:

((sec(x))^2)/tan(x)

Step-by-step explanation:

Computing first derivative

∂(log(tan(x))/∂x

Applying differentiation rule

∂(log(f))/∂x=(∂f/∂x)/f

which gives us

(∂(tan(x))/∂x)/tan(x)

Applying differentiation rule

∂(tan(x))/∂x = (sec(x))^2

therefore we get

((sec(x))^2)/tan(x)

Final simplification

∂f/∂x=((secx)^2)/tanx