Question
Asked Nov 29, 2019
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4. a. Find the derivate of the following functions
for each part)
ptan2(x)
sin(vt1) dt
Fte)-
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4. a. Find the derivate of the following functions for each part) ptan2(x) sin(vt1) dt Fte)-

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Expert Answer

Step 1

To find the derivative of given function.

pian'x
sin(t+1)dt
F(x)
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pian'x sin(t+1)dt F(x)

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Step 2

In order to find the derivative of given function, we use the following rules:

(1) Leibniz integral rule:
Вс3)
d
d(a(x)
2- f(a(x))x-
dc
dt + f(b(x))x
dx
a(x)
dx
a(x)
d
(2) Power Rule
(x*)= a-x*
d
(tan x) = sec2 (x)
(3)
dx
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(1) Leibniz integral rule: Вс3) d d(a(x) 2- f(a(x))x- dc dt + f(b(x))x dx a(x) dx a(x) d (2) Power Rule (x*)= a-x* d (tan x) = sec2 (x) (3) dx

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Step 3

On solving, w...

d
tan x
sin t1dt
dx
tandsint+1))
d(tan x) f-1)x
dtf(tan2 x)x
dx
dx
dc
trdsint+1
d(tan x)f-1)x-
dt f(tan2 x)x
dx
dx
tan2x
(dë-1=
x
0 dtsin
tan x+1x2 tan (x)sec- (x)- sin
-1+1 |x
Vx2-1
x
0+2sin(sec). tan.x-sec2x- sin
-1+1
_
x
-2sin(secx) tanx sec2x-sin
1 1
-1
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d tan x sin t1dt dx tandsint+1)) d(tan x) f-1)x dtf(tan2 x)x dx dx dc trdsint+1 d(tan x)f-1)x- dt f(tan2 x)x dx dx tan2x (dë-1= x 0 dtsin tan x+1x2 tan (x)sec- (x)- sin -1+1 |x Vx2-1 x 0+2sin(sec). tan.x-sec2x- sin -1+1 _ x -2sin(secx) tanx sec2x-sin 1 1 -1

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Tagged in

Math

Calculus