Question

Find the first partial derivatives of the function f(x, t) = e⁽⁻⁵ᵗ⁾ cos(x)?

Answer 1

To find the first partial derivatives of the function f(x, t) = e⁽⁻⁵ᵗ⁾ cos(x), differentiate the function with respect to x and t separately. The partial derivative with respect to x is -sin(x) and the partial derivative with respect to t is -5e⁽⁻⁵ᵗ⁾.

Step-by-step explanation:

To find the first partial derivatives of the function f(x, t) = e⁽⁻⁵ᵗ⁾ cos(x), we differentiate the function with respect to x and t separately.

For the partial derivative with respect to x, we treat t as a constant. So, the derivative of cos(x) with respect to x is -sin(x).

For the partial derivative with respect to t, we treat x as a constant. So, the derivative of e⁽⁻⁵ᵗ⁾ with respect to t is -5e⁽⁻⁵ᵗ⁾.