f is a twice differentiable function and that itssecond partial derivatives are continuous.Let h(t)...

f is a twice differentiable function and that its second partial derivatives are continuous.
Let h(t) = f (x(t), y(t)) where x = 2e^t and y = t.
Suppose that f_x(2, 0) = 3, f_y(2, 0) = 2, f_xx(2, 0) = 4, f_yy(2, 0) = 3, and f_xy(2, 0) = 1.

h'(t) = f_x * 2e^t+ f_y

find h''(t) when t = 0.

(I don't understand how for the second partial derivative d/dy (f_y) = d/dt (x) *f_yx + d/dt(y) * f_yy

Could you explain this step for me in the solution. Thank you :)

Expert Solution

milcah answered 2 years ago

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f is a twice differentiable function and that itssecond partial derivatives are continuous.Let h(t)...

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