- 5

- 2

- Problem Statement
- find first and second partial derivative of z= tan (x^2*y^2)

- Relevant Equations
- tan (x^2*y^2)= sin(x^2*y^2)/cos(x^2*y^2)

Quotient rule: z= f/g ------ z'= (f'g - g'f)/g^2

starting with finding the derivative in respect to x, i treated y^2 as constant 'a': z'= [(a*2x*cos a*x^2)(sin a*x^2) - (- a*2x*sin ax^2)]/cos(a*x^2)^2=

[(a*2x*cos a*x^2)(sin a*x^2)+(a*2x*sin ax^2)]/cos(a*x^2)^2

For the derivative in respect to y it would be the same process, how do i go from here to finding the second derivative?

starting with finding the derivative in respect to x, i treated y^2 as constant 'a': z'= [(a*2x*cos a*x^2)(sin a*x^2) - (- a*2x*sin ax^2)]/cos(a*x^2)^2=

[(a*2x*cos a*x^2)(sin a*x^2)+(a*2x*sin ax^2)]/cos(a*x^2)^2

For the derivative in respect to y it would be the same process, how do i go from here to finding the second derivative?