Question

if y=x-x^2, then the derivative of y^2w.r.t.x^2 is​

Answer 1

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

Answer 2

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