Question

if x=3at and y=at^6 then dy/dx is equal to
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Answer 1

Answer :

dy/dx = 2t⁵

Solution :

• Given : x = 3at , y = at⁶
• To find : dy/dx

We have ,

x = 3at

Now ,

Differentiating both the sides with respect to t , we get ;

=> dx/dt = d(3at)/dt

=> dx/dt = 3a•dt/dt

=> dx/dt = 3a•1

=> dx/dt = 3a -------(1)

Also ,

y = at^6

Now ,

Differentiating both the sides with respect to t , we get ;

=> dy/dt = d(at⁶)/dt

=> dy/dt = a•d(t⁶)/dt

=> dy/dt = a•6t⁵

=> dy/dt = 6at⁵ ------(2)

Now ,

Dividing the eq-(2) by eq-(1) , we get ;

=> (dy/dt)/(dx/dt) = (6at⁵)/3a

=> (dy/dt)•(dt/dx) = 2t⁵

=> dy/dx = 2t⁵

Hence ,

dy/dx = 2t⁵