Question
Asked Oct 4, 2019
2. Calculate the derivative of y = arccos(e
arcsin(x2)
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2. Calculate the derivative of y = arccos(e arcsin(x2)

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check_circleExpert Solution
Step 1

Let u=arcacos(e^x) and v=arcsin(x^2), then y=u/v

arccos(e
arcsin (x2
y
u arccos(e),v = aresin(x2)
y-
V
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arccos(e arcsin (x2 y u arccos(e),v = aresin(x2) y- V

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Step 2

Then , we find du/dx and dv/dx by using result that derivative of arcinx with respect to x is  1/ sqrt(1-x^2) and that of arccosx is -1/ sqrt(1-x^2)

du
d
1
e
2 dx
V1-e2
x
1-(e
dv
1
d
)
2.x
2 dx
dx
vi-x*
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du d 1 e 2 dx V1-e2 x 1-(e dv 1 d ) 2.x 2 dx dx vi-x*

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Step 3

Now qotient rule of differenti...

и
У
du
dv
-u-
dx
dx
dy
2
dx
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и У du dv -u- dx dx dy 2 dx

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Tagged in

Math

Calculus

Derivative