Question
Asked Oct 24, 2019

Find the derivative and second derivative of g(x)=x(100-x^2)^(1/2).

check_circleExpert Solution
Step 1

Since the placement of the radical sign is not clear whether it includes x or no, the question has been solved considering the below given expression.

First derivative,

g(x)x(100-x2
Taking derivative with respect to x
d
(100-x)
dx
dx
Apply the product rule,
(fg)' fg+f.g
d
100-x2(100-x2)
g x)x
dx
dx
d
1
(100-x2)+/(100- x2)-1
= x
2(100-x2)
help_outline

Image Transcriptionclose

g(x)x(100-x2 Taking derivative with respect to x d (100-x) dx dx Apply the product rule, (fg)' fg+f.g d 100-x2(100-x2) g x)x dx dx d 1 (100-x2)+/(100- x2)-1 = x 2(100-x2)

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Step 2

Simplify the expression,

1
(-2х)+ 100-х?):
g () — х.—
2,(100- х*)
-2x2
(100-х)
g(x)=
f100-х")
х?
|8 ()- 100-х).
(100-х )
help_outline

Image Transcriptionclose

1 (-2х)+ 100-х?): g () — х.— 2,(100- х*) -2x2 (100-х) g(x)= f100-х") х? |8 ()- 100-х). (100-х )

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Step 3

Second deriva...

Taking derivative with respect to x
d
d
(100-x2)
Y100-x
dx
g")10
(100-x
d
100-x
dx
Using the quotient rule for second bracket
f
fig-f.g'
(100-x:)·은(12)-x
100-x2
dx
d
1
(100-x2)
d
g"(x)
2{100-x-")
100
help_outline

Image Transcriptionclose

Taking derivative with respect to x d d (100-x2) Y100-x dx g")10 (100-x d 100-x dx Using the quotient rule for second bracket f fig-f.g' (100-x:)·은(12)-x 100-x2 dx d 1 (100-x2) d g"(x) 2{100-x-") 100

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Calculus

Derivative

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