Question

Let f(x, y)=5 e^9 xsin (2 y)
[ ∂ f/∂ x=__; ∂ f/∂ y= __]

Answer 1

The student requests the partial derivatives of the function f(x, y) = 5e^9xsin(2y). The first partial derivative with respect to x is 45e^9xsin(2y), and the second with respect to y is 10e^9xcos(2y).

Step-by-step explanation:

The student asks for the partial derivatives of the function f(x, y) = 5e9xsin(2y) with respect to x and y. To find the partial derivative ∂f/∂x, apply the product rule to the exponential and sine functions, treating y as a constant. Differentiating with respect to x gives us ∂f/∂x = 45e9xsin(2y). For the partial derivative ∂f/∂y, again apply the product rule, this time treating x as a constant, which results in ∂f/∂y = 10e9xcos(2y).