Question

If
z= sin(x-y)
2-3t
y = 4t show that
dz/dt=3/√1-t^2​

Answer 1

Step-by-step explanation:

The given information is: u=sin

−1

(x−y), x=3t and y=4t

3

Substituting the values of x and y in the function u we get,

⇒u=sin

−1

(3t−4t

3

)

Differentiating with respect to t we get,

⇒

dt

du

=

1−(3t−4t

3

)

2

3−12t

2

⇒

dt

du

=

1−t

2

(3−4t

2

)

2

3−12t

2

⇒

dt

du

=

1−t

2

(9+16t

4

−24t

2

)

3−12t

2

⇒

dt

du

=

1−9t

2

−16t

6

+24t

4

3−12t

2

Let us take t

2

=z so that the quation changes to a cubic equation.

⇒

dt

du

=

1−9z−16z

3

+24z

2

3−12t

2

⇒

dt

du

=

−(z−1)(4z−1)

2

3−12t

2

⇒

dt

du

=

1−z

(4z−1)

3(4z−1)

⇒

dt

du

=

1−z

3

⇒

dt

du

=

1−t

2

3