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Calculus Implicit Derivatives November 18 Flashcards | StudBud

Explore/Calculus Implicit Derivatives November 18

Calculus Implicit Derivatives November 18

8 terms·StudBud Administration·23 plays

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Questions 8

Answers

1
Find dy/dx by implicit differentiation: 1 = 3x + 2x²y²
y'=\frac{3-4xy^2}{4x^2y}
y'=\left(3+4xy^2\right)
y'=\frac{3+4xy^2}{2x^2-2y}
y'=\frac{-3-4xy^2}{4x^2y}
2
Find dy/dx by implicit differentiation: sinx + 2cos3y = 5
y'=\frac{\cos x}{18\sin y}
y'=\frac{\cos x}{6\sin\left(3y\right)}
y'=\frac{\sin x}{6\cos\left(3y\right)}
y'=\frac{\cos x}{\sin\left(3y\right)}
3
Find the derivative.
y'=-\frac{2xy}{x^2+1}
y'=\frac{2xy}{x^2+1}
y'=-\frac{xy}{x^2+1}
y'=-\frac{2y}{x}
4
Find dy/dx by implicit differentiation: x² + y²= 9
y'=-\frac{x}{y}
y'=\frac{x}{y}
y'=-\frac{y}{x}
y'=-\frac{2x}{y}
5
Find the derivative.
y'=5\sin^4\left(4x\right)\cos\left(4x\right)
y'=20\sin^4\left(4x\right)\cos\left(4x\right)
y'=5\sin^4\left(4x\right)
y'=-20\sin^4\left(4x\right)\cos\left(4x\right)
6
Find dy/dx by implicit differentiation: x⁴ + x²y² = y²
y'=\frac{-2x^2-xy}{xy}
y'=\frac{xy^2+2x^3}{y-x^2y}
y'=\frac{xy^2+2x^3}{y+x^2y}
y'=\frac{-xy^2-2x^3}{y-x^2y}
7
Find the derivative.
y'=\frac{-3}{\left(x^2+3\right)^4}
y'=-\frac{6x}{\left(x^2+3\right)^2}
y'=\frac{x}{x^2+3}
y'=-\frac{6x}{\left((x^2+3\right)^4}
8
Which of the following will require implicit differentiation?
y=20
y=4x-8
5xy=25y2
y=x