RD Sharma Class 12 Solutions - Higher Order Derivatives | Mathematics (Maths) Class 12 - JEE PDF Download

 Page 1


12. Higher Order Derivatives
Exercise 12.1
26. Question
If y = tan 
– 1
 x, show that (1 + x
2
) .
Answer
Formula: –
Given: –
Y = tan 
– 1
x
Differentiating w.r.t x
Using formula(ii)
Again Differentiating w.r.t x
Using formula(iii)
Hence proved.
27. Question
If y = {log (x + vx
2
 + 1)
2
, show that (1 + x
2
) .
Answer
Formula: –
Page 2


12. Higher Order Derivatives
Exercise 12.1
26. Question
If y = tan 
– 1
 x, show that (1 + x
2
) .
Answer
Formula: –
Given: –
Y = tan 
– 1
x
Differentiating w.r.t x
Using formula(ii)
Again Differentiating w.r.t x
Using formula(iii)
Hence proved.
27. Question
If y = {log (x + vx
2
 + 1)
2
, show that (1 + x
2
) .
Answer
Formula: –
Given: –
Differentiating w.r.t x
Using formula(ii)
Using formula(i)
Squaring both sides
Differentiating w.r.t x
Using formual(iii)
Hence proved
28. Question
If y = (tan 
– 1
 x)
2
, then prove that (1 – x2)
2
 y
2
 + 2x (1 + x
2
) y
1
 = 2
Answer
Formula: –
Given: –
Y = (tan 
– 1
x)
2
Then
Page 3


12. Higher Order Derivatives
Exercise 12.1
26. Question
If y = tan 
– 1
 x, show that (1 + x
2
) .
Answer
Formula: –
Given: –
Y = tan 
– 1
x
Differentiating w.r.t x
Using formula(ii)
Again Differentiating w.r.t x
Using formula(iii)
Hence proved.
27. Question
If y = {log (x + vx
2
 + 1)
2
, show that (1 + x
2
) .
Answer
Formula: –
Given: –
Differentiating w.r.t x
Using formula(ii)
Using formula(i)
Squaring both sides
Differentiating w.r.t x
Using formual(iii)
Hence proved
28. Question
If y = (tan 
– 1
 x)
2
, then prove that (1 – x2)
2
 y
2
 + 2x (1 + x
2
) y
1
 = 2
Answer
Formula: –
Given: –
Y = (tan 
– 1
x)
2
Then
Using formula (ii)&(i)
Again differentiating with respect to x on both the sides,we obtain
 using formula(i)&(iii)
Hence proved.
29. Question
If y = cot x show that .
Answer
Formula: –
Given: –
Y = cotx
Differentiating w.r.t. x
Using formula (ii)
Differentiating w.r.t x
Using formual (iii)
Page 4


12. Higher Order Derivatives
Exercise 12.1
26. Question
If y = tan 
– 1
 x, show that (1 + x
2
) .
Answer
Formula: –
Given: –
Y = tan 
– 1
x
Differentiating w.r.t x
Using formula(ii)
Again Differentiating w.r.t x
Using formula(iii)
Hence proved.
27. Question
If y = {log (x + vx
2
 + 1)
2
, show that (1 + x
2
) .
Answer
Formula: –
Given: –
Differentiating w.r.t x
Using formula(ii)
Using formula(i)
Squaring both sides
Differentiating w.r.t x
Using formual(iii)
Hence proved
28. Question
If y = (tan 
– 1
 x)
2
, then prove that (1 – x2)
2
 y
2
 + 2x (1 + x
2
) y
1
 = 2
Answer
Formula: –
Given: –
Y = (tan 
– 1
x)
2
Then
Using formula (ii)&(i)
Again differentiating with respect to x on both the sides,we obtain
 using formula(i)&(iii)
Hence proved.
29. Question
If y = cot x show that .
Answer
Formula: –
Given: –
Y = cotx
Differentiating w.r.t. x
Using formula (ii)
Differentiating w.r.t x
Using formual (iii)
Hence proved.
30. Question
Find , where y = log .
Answer
Formula: –
Given: –
Differentiating w.r.t x
Again Differentiating w.r.t x
31. Question
If y = e
x
(sin x + cos x) prove that .
Answer
Formula: –
Given: –
Page 5


12. Higher Order Derivatives
Exercise 12.1
26. Question
If y = tan 
– 1
 x, show that (1 + x
2
) .
Answer
Formula: –
Given: –
Y = tan 
– 1
x
Differentiating w.r.t x
Using formula(ii)
Again Differentiating w.r.t x
Using formula(iii)
Hence proved.
27. Question
If y = {log (x + vx
2
 + 1)
2
, show that (1 + x
2
) .
Answer
Formula: –
Given: –
Differentiating w.r.t x
Using formula(ii)
Using formula(i)
Squaring both sides
Differentiating w.r.t x
Using formual(iii)
Hence proved
28. Question
If y = (tan 
– 1
 x)
2
, then prove that (1 – x2)
2
 y
2
 + 2x (1 + x
2
) y
1
 = 2
Answer
Formula: –
Given: –
Y = (tan 
– 1
x)
2
Then
Using formula (ii)&(i)
Again differentiating with respect to x on both the sides,we obtain
 using formula(i)&(iii)
Hence proved.
29. Question
If y = cot x show that .
Answer
Formula: –
Given: –
Y = cotx
Differentiating w.r.t. x
Using formula (ii)
Differentiating w.r.t x
Using formual (iii)
Hence proved.
30. Question
Find , where y = log .
Answer
Formula: –
Given: –
Differentiating w.r.t x
Again Differentiating w.r.t x
31. Question
If y = e
x
(sin x + cos x) prove that .
Answer
Formula: –
Given: –
Differentiating w.r.t x
Differentiating w.r.t x
Adding and subtracting  on RHS
32. Question
If y = e
x
 (sin x + cos x) Prove that 
Answer
Formula: –
Given: –
y = e
x
(sinx + cosx)
differentiating w.r.t x