Implicit Differentiation, 9

Category: Differential Calculus, Algebra

"Published in Vacaville, California, USA"

Find dy/dx and d²y/dx² by implicit differentiation for:

Solution:

Consider the given equation above

Take the first derivative of the given equation with respect to x by implicit differentiation, we have 

Finally, take the second derivative of the above equation with respect to x by implicit differentiation, we have

but

Hence, the above equation becomes  

We can further simplify the above equation by using the given equation as follows  

Therefore,

 

Implicit Differentiation, 8

Category: Differential Calculus, Algebra

"Published in Vacaville, California, USA"

Find dy/dx and d²y/dx² by implicit differentiation for:

Solution:

Consider the given equation above

Take the first derivative of the given equation with respect to x by implicit differentiation, we have 

Finally, take the second derivative of the above equation with respect to x by implicit differentiation, we have

but

Hence, the above equation becomes 

We can further simplify the above equation by using the given equation as follows 

Therefore,