estion: Find the derivative of the following 1. function: y = In vtan x

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.3: The Chain Rule
Problem 65E
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3.3.1. Derivatives of Logarithmic Functions
The derivative of the logarithmic function is determined by the
following theorem.
Theorem 3.3 Chain Rule of the Derivative of Logarithmic Function
Let a be a positive real number (a # 1) and let u be a differentiable
function of x and u(x) > 0, then
1 du
и dx
du
(loga u)
(In u)
dx
(In a)u dx
dx
The second formula is a special case of the first formula since the
natural logarithm In u = log, u.
In the first formula we can set
a = e thus In a = In e = 1.
Question:
1. Find the derivative of the following
function:
y = ln vtan x
Transcribed Image Text:3.3.1. Derivatives of Logarithmic Functions The derivative of the logarithmic function is determined by the following theorem. Theorem 3.3 Chain Rule of the Derivative of Logarithmic Function Let a be a positive real number (a # 1) and let u be a differentiable function of x and u(x) > 0, then 1 du и dx du (loga u) (In u) dx (In a)u dx dx The second formula is a special case of the first formula since the natural logarithm In u = log, u. In the first formula we can set a = e thus In a = In e = 1. Question: 1. Find the derivative of the following function: y = ln vtan x
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