GATE 2023 II Engg. Mathematics Quiz 1

Let z = f (x, y) where x, y are function of t then according to the chain rule is equal to

Value of

Consider a function f(x, y, z) given by f(x, y, z) = (x² – y² + 9z²) (2y² – z²) The partial derivative of this function with respect to x at the point
x =1, y = 1 and z = 1 is____.

The smallest positive integers n for which

If find the value of

The definite integral