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Tuomo
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I have derivative dx/dt = y(u(t)) * z(u(t)) + u(t)
Now, what is dx/du ? I know the chain rule should help, but I am stuck :-(
Now, what is dx/du ? I know the chain rule should help, but I am stuck :-(
Tuomo said:I have derivative dx/dt = y(u(t)) * z(u(t)) + u(t)
Now, what is dx/du ? I know the chain rule should help, but I am stuck :-(
fluidistic said:Maybe [itex]\frac{dx}{du}=\frac{dx}{dt} \cdot \frac{dt}{du}[/itex].
The chain rule for implicit differentiation is a method used to find the derivative of a function that is implicitly defined. It is used when a function is expressed in terms of both dependent and independent variables, and the dependent variable is not explicitly stated.
The chain rule is applied by first identifying the dependent and independent variables in the function. Then, the derivative of the dependent variable is found with respect to the independent variable. Finally, the derivative of the independent variable is multiplied by the derivative of the dependent variable, giving the final result.
The chain rule is important because it allows us to find the derivative of a function that is not explicitly defined in terms of its dependent variable. This is especially useful in situations where it is difficult or impossible to solve for the dependent variable explicitly.
One common mistake is to forget to apply the chain rule and instead use the power rule or product rule. Another mistake is to forget to use the derivative of the dependent variable when multiplying by the derivative of the independent variable.
Yes, the chain rule can also be applied in other types of differentiation, such as logarithmic, exponential, and trigonometric functions. It is a fundamental rule in calculus and is used to find the derivative of composite functions.