Video ExampleDifferentiate y = x7VxEXAMPLE 8Since both the base and the exponent are variable, we use logarithmicSOLUTIONdifferentiation:In(2)77Vx In(x)In y=y'7VXУ(In(x))7 In(x)у' %3D Уx'Vx7VXeln(x)Another method is to write x7Vx =dddxdxd7x In(x)dxx7Vx=yIn(x2-4x +1), (4, 0)

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Asked Oct 11, 2019
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Video Example
Differentiate y = x7Vx
EXAMPLE 8
Since both the base and the exponent are variable, we use logarithmic
SOLUTION
differentiation:
In(2)7
7Vx In(x)
In y
=
y'
7VX
У
(In(x))
7 In(x)
у' %3D У
x'Vx
7VX
eln(x)
Another method is to write x7Vx =
d
d
dx
dx
d
7x In(x)
dx
x7Vx
=
yIn(x2-4x +1), (4, 0)
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Video Example Differentiate y = x7Vx EXAMPLE 8 Since both the base and the exponent are variable, we use logarithmic SOLUTION differentiation: In(2)7 7Vx In(x) In y = y' 7VX У (In(x)) 7 In(x) у' %3D У x'Vx 7VX eln(x) Another method is to write x7Vx = d d dx dx d 7x In(x) dx x7Vx = yIn(x2-4x +1), (4, 0)

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Expert Answer

Step 1

To determine the logarithmic derivative and exponential derivative of the function.

Step 2

Given:

y =
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y =

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Step 3

Formula used:

...
In(a*)nln a
(s())(8(x) g'(x)
dx
d
(5 (x)-g(x))= 5'(x),g (x)+ f (x)g \(x)
dx
(x*)= nm*
n
dx
d
1
(In x
x
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In(a*)nln a (s())(8(x) g'(x) dx d (5 (x)-g(x))= 5'(x),g (x)+ f (x)g \(x) dx (x*)= nm* n dx d 1 (In x x

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Tagged in

Math

Calculus

Derivative