RD Sharma Class 12 Solutions - Differentiation - 2

# RD Sharma Class 12 Solutions - Differentiation - 2 | Mathematics (Maths) Class 12 - JEE PDF Download

``` Page 1

27. Question
Find , when
y = (tan x)
cot x
+ (cot x)
tan x
let y = (tan x)
cot x
+ (cot x)
tan x
? y = a + b
where a= (tan x)
cot x
; b = (cot x)
tan x
a= (tan x)
cot x
Taking log both the sides:
? log a= log (tan x)
cot x
? log a= cot x log (tan x)
{log x
a
= alog x}
Differentiating with respect to x:
b = (cot x)
tan x
Page 2

27. Question
Find , when
y = (tan x)
cot x
+ (cot x)
tan x
let y = (tan x)
cot x
+ (cot x)
tan x
? y = a + b
where a= (tan x)
cot x
; b = (cot x)
tan x
a= (tan x)
cot x
Taking log both the sides:
? log a= log (tan x)
cot x
? log a= cot x log (tan x)
{log x
a
= alog x}
Differentiating with respect to x:
b = (cot x)
tan x
Taking log both the sides:
? log b= log (cot x)
tan x
? log b= tan x log (cot x)
{log x
a
= alog x}
Differentiating with respect to x:
28. Question
Find , when
? y = a + b
Page 3

27. Question
Find , when
y = (tan x)
cot x
+ (cot x)
tan x
let y = (tan x)
cot x
+ (cot x)
tan x
? y = a + b
where a= (tan x)
cot x
; b = (cot x)
tan x
a= (tan x)
cot x
Taking log both the sides:
? log a= log (tan x)
cot x
? log a= cot x log (tan x)
{log x
a
= alog x}
Differentiating with respect to x:
b = (cot x)
tan x
Taking log both the sides:
? log b= log (cot x)
tan x
? log b= tan x log (cot x)
{log x
a
= alog x}
Differentiating with respect to x:
28. Question
Find , when
? y = a + b
a = (sin x)
x
Taking log both the sides:
? log a= log (sin x)
x
? log a= x log (sin x)
{log x
a
= alog x}
Differentiating with respect to x:
Put the value of a= (sin x)
x
:
Differentiating with respect to x:
Page 4

27. Question
Find , when
y = (tan x)
cot x
+ (cot x)
tan x
let y = (tan x)
cot x
+ (cot x)
tan x
? y = a + b
where a= (tan x)
cot x
; b = (cot x)
tan x
a= (tan x)
cot x
Taking log both the sides:
? log a= log (tan x)
cot x
? log a= cot x log (tan x)
{log x
a
= alog x}
Differentiating with respect to x:
b = (cot x)
tan x
Taking log both the sides:
? log b= log (cot x)
tan x
? log b= tan x log (cot x)
{log x
a
= alog x}
Differentiating with respect to x:
28. Question
Find , when
? y = a + b
a = (sin x)
x
Taking log both the sides:
? log a= log (sin x)
x
? log a= x log (sin x)
{log x
a
= alog x}
Differentiating with respect to x:
Put the value of a= (sin x)
x
:
Differentiating with respect to x:
29 A. Question
Find , when
y = x
cos x
+ (sin x)
tan x
let y = x
cos x
+ (sin x)
tan x
? y = a + b
where a= x
cos x
; b = (sin x)
tan x
a= x
cos x
Taking log both the sides:
? log a= log (x)
cos x
? log a= cos x log x
{log x
a
= alog x}
Differentiating with respect to x:
Page 5

27. Question
Find , when
y = (tan x)
cot x
+ (cot x)
tan x
let y = (tan x)
cot x
+ (cot x)
tan x
? y = a + b
where a= (tan x)
cot x
; b = (cot x)
tan x
a= (tan x)
cot x
Taking log both the sides:
? log a= log (tan x)
cot x
? log a= cot x log (tan x)
{log x
a
= alog x}
Differentiating with respect to x:
b = (cot x)
tan x
Taking log both the sides:
? log b= log (cot x)
tan x
? log b= tan x log (cot x)
{log x
a
= alog x}
Differentiating with respect to x:
28. Question
Find , when
? y = a + b
a = (sin x)
x
Taking log both the sides:
? log a= log (sin x)
x
? log a= x log (sin x)
{log x
a
= alog x}
Differentiating with respect to x:
Put the value of a= (sin x)
x
:
Differentiating with respect to x:
29 A. Question
Find , when
y = x
cos x
+ (sin x)
tan x
let y = x
cos x
+ (sin x)
tan x
? y = a + b
where a= x
cos x
; b = (sin x)
tan x
a= x
cos x
Taking log both the sides:
? log a= log (x)
cos x
? log a= cos x log x
{log x
a
= alog x}
Differentiating with respect to x:
b = (sin x)
tan x
Taking log both the sides:
? log b= log (sin x)
tan x
? log b= tan x log (sin x)
{log x
a
= alog x}
Differentiating with respect to x:
29 B. Question
Find , when
y = x
x
+ (sin x)
x
let y = x
x
+ (sin x)
x
```

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

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