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Questions and Answers
What is the derivative of √8 + x√x?
What is the derivative of √8 + x√x?
- 4√x + 1/√x
- 3√x + √x
- 2√x + 1/√x (correct)
- 1/2√x + 1/2√x
For y = (x + 1)(x - 2), what is the correct derivative?
For y = (x + 1)(x - 2), what is the correct derivative?
- 2x + 3
- 3x² + 2x - 2 (correct)
- 3x² + 2x + 2
- 3x² - 2x + 2
If ax + by = ab, what is the correct expression for dy/dx?
If ax + by = ab, what is the correct expression for dy/dx?
- by (correct)
- 2by
- by (correct)
- bx
What is the derivative of tan x with respect to cot x?
What is the derivative of tan x with respect to cot x?
If y = tan⁻¹(cos 2x), what is dy/dx?
If y = tan⁻¹(cos 2x), what is dy/dx?
What is the nth derivative of $2e^{x}$?
What is the nth derivative of $2e^{x}$?
If $xy=k^{2}$, what is y"?
If $xy=k^{2}$, what is y"?
What is the 3rd order derivative of $2^{x}$?
What is the 3rd order derivative of $2^{x}$?
For $f(x)=Ax+B\cos(x)$, what is the 2nd order derivative?
For $f(x)=Ax+B\cos(x)$, what is the 2nd order derivative?
What is the nth derivative of $2e^{x}$?
What is the nth derivative of $2e^{x}$?
If $xy=k^{2}$, what is the second derivative of y with respect to x?
If $xy=k^{2}$, what is the second derivative of y with respect to x?
What is the 3rd order derivative of $2^{x}$?
What is the 3rd order derivative of $2^{x}$?
If $S$ represents the distance covered by a car, what does $\frac{d^{2}S}{dt^{2}}$ represent?
If $S$ represents the distance covered by a car, what does $\frac{d^{2}S}{dt^{2}}$ represent?
What is the nth derivative of $2e^{x}$?
What is the nth derivative of $2e^{x}$?
In the function $f(x)=Ax+B\cos(x)$, what is the 2nd order derivative?
In the function $f(x)=Ax+B\cos(x)$, what is the 2nd order derivative?
If $y=tan^{-1}x$, what is $y''(1)$?
If $y=tan^{-1}x$, what is $y''(1)$?
What does $y=x-\frac{x^3}{3!}+\frac{x^5}{5!}-...$ represent in terms of series?
What does $y=x-\frac{x^3}{3!}+\frac{x^5}{5!}-...$ represent in terms of series?
If $S$ represents the distance covered by a car, what does $\frac{d^2S}{dt^2}$ represent?
If $S$ represents the distance covered by a car, what does $\frac{d^2S}{dt^2}$ represent?
What is the third order derivative of $2^{x}$?
What is the third order derivative of $2^{x}$?
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Study Notes
Differentiation
- The derivative of √8+ xvx is not provided.
- If y=(x+1)(x-2), then y' = 2x - 1.
Second Derivative
- If y=tan⁻¹x, then y''(1) = -1/2.
Higher Order Derivatives and Applications
- If S is the distance covered by a car, then d²S/dt² is acceleration.
nth Derivative
- The nth derivative of 2eˣ is 2neˣ.
Implicit Differentiation
- If xy=k², then y" = 2k²/x³.
Applications of Derivatives
- A function f(x) is said to be a decreasing function when x₁ > x₂ implies f(x₁) ≤ f(x₂).
Maclaurin Series
- The Maclaurin series of sinx is x - x³/3! + x⁵/5! - ...
Derivatives of Trigonometric Functions
- The derivative of tanx is sec²x.
- The derivative of tanh ax is asechax.
- The derivative of coth⁻¹(2x) is 2/(1 - 4x²).
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