if y=x-x^2, then the derivative of y^2w.r.t.x^2 is
Answers
Answered by
2
Step-by-step explanation:
ANSWER
Given, y=x−x
2
On differentiating w.r.t. x, we get
dx
dy
=1−2x
Now,
d(x
2
)
d(y
2
)
=
d(x
2
)
dx
d(y
2
)
d(x)
=
2x
2y
dx
dy
=2y
2x
(1−2x)
=
2x
2(x−x
2
)(1−2x)
=(1−x)(1−2x)
=1−3x+2x
2
=2x
2
−3x+1.
Hope so it may help you
Answered by
3
Step-by-step explanation:
y=cos
−1
cosx
dx
dy
=
dx
d
(cos
−1
(cos(x)))
Let f=cos
−1
(u),u=cos(x)
=
du
d
(cos
−1
(u))
dx
d
(cos(x))
=(−
1−u
2
1
)(−sin(x))
=(−
1−cos
2
(x)
1
)(−sin(x))
∴
dx
dy
=
sin
2
(x)
sin(x)
dx
dy
x=
4
5π
=
sin
2
(
4
5π
)
sin(
4
5π
)
=
1−cos(
2
π
)
2
sin(
4
5π
)
=
1−0
2
(−
2
2
)
=−1
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