differentiation derivative of logarithmic function
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Differentiation
Derivative of
Logarithmic Function
Differentiation
We take the natural logarithm of both sides of the equation y = ( f (x))g(x), to btain
ln y = ln ( f (x))g(x) = g(x) ln f (x)
Then we differentiate implicitly both sides of the resulting equation ln y = g(x) ln f (x) with respect to x.
Logarithmic Differentiation The Function y = ( f (x)) g (x)
Differentiation
PROPERTIES OF THE NATURAL LOGARITHM
Differentiation
Example 1:
Solution
Differentiation
Example 2: Differentiate y = xx
Solution Apply the natural logarithm to both sides of this equation getting
Differentiate both sides of this equation.
Multiply both sides of this equation by y, getting
Differentiation
Example 3: Differentiate
Solution
Differentiation
Example 4: Differentiate Solution
Differentiation
Example 5: Differentiate
Solution
Differentiation
Derivative of Logarithmic Function
ASSESSMENT
Differentiation
Using logarithmic differentiation, differentiate:
a:
b:
c:
d:
Differentiation
e:
f:
Differentiation
a:
b:
c:
d:
Solutions:
Differentiation
e:
f:
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