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Find y' and y".y x In(x)у"y'"

Question
Find y' and y".
y x In(x)
у"
y'"
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Find y' and y". y x In(x) у" y'"

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Step 1

To find the first and second derivatives of the given function

y= n (x)
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y= n (x)

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Step 2

Since the function is a product of two functions, so we’ll use the following rules of derivatives:

(x)(x))x) 8(x)+ f(x)g(x)
Product rule:
f(x)g (x)f(x)-s (x). g'(x)
dg(x)
d
Quotient rule:
g (x)
d
n-1
Power rule:
=nx"-
d
(Inx)
Standarad derivatives:
x
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(x)(x))x) 8(x)+ f(x)g(x) Product rule: f(x)g (x)f(x)-s (x). g'(x) dg(x) d Quotient rule: g (x) d n-1 Power rule: =nx"- d (Inx) Standarad derivatives: x

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Step 3

To find the first derivative, using the product ru...

y'=() Inx(x)
1
1
In x
2
1
|-In x
1
In x
2
2x2x
In x 2
2x
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y'=() Inx(x) 1 1 In x 2 1 |-In x 1 In x 2 2x2x In x 2 2x

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Math

Calculus

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