Equation 6 is a formula for the derivative dy / dx of a function defined implicitly by an equation F ( x , y ) = 0, provided that F is differentiable and F y ≠ 0. Prove that if F has continuous second derivatives, then a formula for the second derivative of y is d 2 y d x 2 = − F x x F 2 y − 2 F x y F x F y + F y y F 2 x F 3 y
Equation 6 is a formula for the derivative dy / dx of a function defined implicitly by an equation F ( x , y ) = 0, provided that F is differentiable and F y ≠ 0. Prove that if F has continuous second derivatives, then a formula for the second derivative of y is d 2 y d x 2 = − F x x F 2 y − 2 F x y F x F y + F y y F 2 x F 3 y
Solution Summary: The author explains that the implicit function is F(x,y)=0.
Equation 6 is a formula for the derivative dy/dx of a function defined implicitly by an equation F(x, y) = 0, provided that F is differentiable and Fy ≠ 0. Prove that if F has continuous second derivatives, then a formula for the second derivative of y is
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=
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F
2
y
−
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F
x
y
F
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y
+
F
y
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F
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With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
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