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UPSC NDA Math Model Paper 8
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© examsnet.com
Question : 51
Total: 120
If x = k(θ + sin θ) and y = k (1 + cos θ), then what is the derivative of y with respect to x at θ = π/2?
-1
0
1
2
Validate
Solution:
Given,
x
=
k
(
θ
+
sin
θ
)
⇒
d
x
d
θ
=
k
(
1
+
cos
θ
)
y
=
k
(
1
+
cos
θ
)
⇒
d
y
d
θ
=
k
(
−
sin
θ
)
By chain rule, we have
d
y
d
x
=
d
y
d
θ
d
x
d
θ
⇒
d
y
d
x
=
−
k
sin
θ
k
(
1
+
cos
θ
)
⇒
d
y
d
x
=
−
sin
θ
(
1
+
cos
θ
)
Put θ = π/2
d
y
d
x
=
−
sin
π
2
(
1
+
cos
π
2
)
⇒
d
y
d
x
=
−
1
Hence, if x = k(θ + sin θ) and y = k (1 + cos θ), then the derivative of y with respect to x at θ = π/2 is -1.
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