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Questions and Answers
Given $y = \tan^{-1}(\frac{4x}{1+5x^2}) + \cot^{-1}(\frac{3-2x}{2+3x})$, determine $\frac{dy}{dx}$.
Given $y = \tan^{-1}(\frac{4x}{1+5x^2}) + \cot^{-1}(\frac{3-2x}{2+3x})$, determine $\frac{dy}{dx}$.
- $\frac{5}{1+25x^2}$
- $0$ (correct)
- $\frac{5}{1-25x^2}$
- $-\frac{5}{1+25x^2}$
If $xy = 1 + \log y$ and $k \frac{dy}{dx} + y^2 = 0$, find an expression for $k$.
If $xy = 1 + \log y$ and $k \frac{dy}{dx} + y^2 = 0$, find an expression for $k$.
- $1 - 2xy$
- $xy - 1$
- $\frac{1}{xy - 1}$ (correct)
- $1 + xy$
If $x = 2at^2$ and $y = at^4$, determine the value of $\frac{d^2y}{dx^2}$ at $t = 2$.
If $x = 2at^2$ and $y = at^4$, determine the value of $\frac{d^2y}{dx^2}$ at $t = 2$.
- $4$
- $\frac{1}{2a}$ (correct)
- $-\frac{1}{2a}$
- $2a$
Given $y = e^{m \sin^{-1} x}$ and $(1 - x^2)(\frac{dy}{dx})^2 = Ay^2$, find the value of $A$.
Given $y = e^{m \sin^{-1} x}$ and $(1 - x^2)(\frac{dy}{dx})^2 = Ay^2$, find the value of $A$.
Determine $\frac{dy}{dx}$ if $y = \tan^{-1}(\frac{4x}{1+5x^2}) + \cot^{-1}(\frac{3-2x}{2+3x})$.
Determine $\frac{dy}{dx}$ if $y = \tan^{-1}(\frac{4x}{1+5x^2}) + \cot^{-1}(\frac{3-2x}{2+3x})$.
Given the equation $xy = 1 + \log y$, and knowing that $k \frac{dy}{dx} + y^2 = 0$, what is the correct expression for $k$?
Given the equation $xy = 1 + \log y$, and knowing that $k \frac{dy}{dx} + y^2 = 0$, what is the correct expression for $k$?
If $x = 2at^2$ and $y = at^4$, calculate $\frac{d^2y}{dx^2}$ at $t = 2$.
If $x = 2at^2$ and $y = at^4$, calculate $\frac{d^2y}{dx^2}$ at $t = 2$.
If $y = e^{m \sin^{-1} x}$ and $(1 - x^2)(\frac{dy}{dx})^2 = Ay^2$, what is the value of $A$?
If $y = e^{m \sin^{-1} x}$ and $(1 - x^2)(\frac{dy}{dx})^2 = Ay^2$, what is the value of $A$?
Determine the value of $\frac{dy}{dx}$ for $y = \tan^{-1}(\frac{4x}{1+5x^2}) + \cot^{-1}(\frac{3-2x}{2+3x})$.
Determine the value of $\frac{dy}{dx}$ for $y = \tan^{-1}(\frac{4x}{1+5x^2}) + \cot^{-1}(\frac{3-2x}{2+3x})$.
For the equation $xy = 1 + \log y$, given $k \frac{dy}{dx} + y^2 = 0$, solve for k.
For the equation $xy = 1 + \log y$, given $k \frac{dy}{dx} + y^2 = 0$, solve for k.
Flashcards
Inverse Trigonometric Functions
Inverse Trigonometric Functions
A function is considered as an inverse trigonometric function when it reverses the operations of the trigonometric functions such as sine, cosine, tangent, cotangent, secant, and cosecant.
Derivatives of Implicit Functions
Derivatives of Implicit Functions
If xy = 1 + log y and k dy/dx + y² = 0, then k is
Parametric Differentiation
Parametric Differentiation
Given x = 2at², y = at⁴, then d²y/dx² at t = 2 is
Chain Rule and Implicit Relations
Chain Rule and Implicit Relations
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Study Notes
- y = tan⁻¹(4x/(1+5x²)) + cot⁻¹((3-2x)/(2+3x)), then dy/dx = 0
- If xy = 1 + log y and k dy/dx + y² = 0, then k is 1/(xy-1)
- If x = 2at², y = at⁴, then d²y/dx² at t = 2 is 1/(2a)
- If y = e^(msin⁻¹x) and (1-x²)(dy/dx)² = Ay², then A = m²
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