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Differentiate y = x³√x Solution 1 Since both the base and the exponent are variable, we use logarithmic differentiation. In(y) = n(+³√x) = 3√x In(x) 1/2 + 3√x ⋅ ( [ • + ³√x ( Solution 2 Another method is to write x³√x = n(x) 3√x (x³√x) = (1 dx •x³√x ( ) + (In(x)) · ( [ 3 In(x) = ])+(³√x In(x)) (as in Solution 1)

Differentiate y = x³√x Solution 1 Since both the base and the exponent are variable, we use logarithmic differentiation. In(y) = n(+³√x) = 3√x In(x) 1/2 + 3√x ⋅ ( [ • + ³√x ( Solution 2 Another method is to write x³√x = n(x) 3√x (x³√x) = (1 dx •x³√x ( ) + (In(x)) · ( [ 3 In(x) = ])+(³√x In(x)) (as in Solution 1)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 17E
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Example 8 Video Example Differentiate y = x³√x Solution 1 Since both the base and the exponent are variable, we use logarithmic differentiation. In(y) = In (x³√x) = 3√x In(x) = = 3√x. ([ y Solution 2 Another method is to write x³√x = ln(x) 3√x e d & (+³√x) = dx d dx + (In(x)). 3 In(x) = ³√x ( [ 1) (3√x In(x)) (as in Solution 1)
Transcribed Image Text:Example 8 Video Example Differentiate y = x³√x Solution 1 Since both the base and the exponent are variable, we use logarithmic differentiation. In(y) = In (x³√x) = 3√x In(x) = = 3√x. ([ y Solution 2 Another method is to write x³√x = ln(x) 3√x e d & (+³√x) = dx d dx + (In(x)). 3 In(x) = ³√x ( [ 1) (3√x In(x)) (as in Solution 1)
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