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Derivatie of f(x(t),t) with respect to t.

User Khalida
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Final answer:

To find the derivative of a function f with respect to t when f is a function of both x and t, we use the chain rule. The derivative is given by ∂f / ∂x dx / dt + ∂f / ∂t. Here, ∂ represents the partial derivative and dx / dt represents the derivative of x(t) with respect to t.

Step-by-step explanation:

The question asks for the derivative of a function f with respect to t when f is a function of both x and t. To find this derivative, we use the chain rule. Let's denote f as f(x(t), t). Using the chain rule, the derivative of f with respect to t is given by:
df(x(t), t)

dt = ∂f / ∂x dx / dt + ∂f / ∂t
Here, ∂ represents the partial derivative and dx / dt represents the derivative of x(t) with respect to t. The terms ∂f / ∂x and ∂f / ∂t are the partial derivatives of f with respect to x and t respectively.

User Zara
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