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Find y'and y".едетy99e*+xу'=+x(e* + 1)9ex9еXу" 3

Question
Find y'and y".
едет
y
99e*+x
у'
=
+x(e* + 1)
9ex
9е
X
у" 3
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Find y'and y". едет y 99e*+x у' = +x(e* + 1) 9ex 9е X у" 3

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check_circleAnswer
Step 1

Given function is:

 

Applying derivative with respect to x:

The chain rule of derivative states:

Applying chain rule:

= e
dy
(a)
dxc
dx
(f(g(x)) f(g(x))(g(x))f(g(x)) g'(x)
dx
dx
d
y'e(9e
y' e(9e
+x
y'=9e°
11
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= e dy (a) dxc dx (f(g(x)) f(g(x))(g(x))f(g(x)) g'(x) dx dx d y'e(9e y' e(9e +x y'=9e° 11

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Step 2

Applying the derivative again and using the chain rule:

(Here, the term in the parent...

d
d
9e
(y') =
dx
dx
d
y"=(9e
(9e +x)
dx
y 9e(9e 1
X
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d d 9e (y') = dx dx d y"=(9e (9e +x) dx y 9e(9e 1 X

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Tagged in

Math

Calculus

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