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How would one solve the equation f '(-2x) + g '(4x) = - x?
To simplify this equation, you can first use the chain rule to find the derivatives of the functions f(-2x) and g(4x). Then, combine like terms and solve for x.
No, the product rule is used to find the derivative of a product of two functions. In this equation, we are given the derivatives of two functions and need to find the value of x.
Yes, there are several methods for solving equations with derivatives, such as the chain rule, product rule, quotient rule, and power rule. It is important to identify which rule(s) can be applied to simplify the equation.
You can check your solution by plugging it back into the original equation and seeing if it satisfies the equation. You can also take the derivative of the solution and compare it to the given derivatives in the equation.
Yes, this equation can have multiple solutions for x. It is important to carefully simplify the equation and check for any extraneous solutions that may arise from applying the derivative rules.