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Explain the differences between computing the derivatives of functions that are defined implicity and explicitly Select each of the following that correctly describes the differences A To compute the derivative of an explicitly defined function y=f(x), use the rules of differentiation to differentiate y with respect to x. To compute the derivative of a function defined implicitly by an equation, write the independent variable y as a function of the dependent variable and x, use the chain nule to differentiate each term of the equation with respect to x, and then solve for dy/dx B. When computing the derivative of an explicitly defined function yfx), the result dy/dx depends only on x. When computing the derivative of an implicitly defined function, the result dy/dx depends only on y C. To compute the derivative of an explicitly defined function y-fx), use the rules of differentation to differentiate y with respect to x. To compute the derivative of any function defined implicity by an equation, solve the equation for y and then differentiate each term of the resulting function with respect to x to find a single definition of dy/dx. When computing the derivative of an explicitly defined function y(x), the result dy/dx depends only on x When computing the derivative of an implicitly defined function, the result dy/dx may depend on both x and y

dy 1 18. Consider the curve x = y' . Use implicit differentiation to verify that = dx Use implicit differentiation d. 18 -y -x=and dx Solve for dy dx Find d'y dx dx 17 18y to find the derivative of each side of the equation. dy dx and then find dx²

a. Use implicit differentiation to find the derivative b. Find the slope of the curve at the given point. sin (y) = 3x³ - 3; (1,π) a. dx = -9 dy dx b. The slope at (1,7) is-9. (Simplify your answer.)

Use implicit differentiation to find dy dx sin (y) + sin (x) = y - cos (x) cos (y) - 1 dy dx