what is the derivative of log tanx base e
Answers
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.
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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