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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
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Nov 21, 2024 Last updated |
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