Podcast
Questions and Answers
What is the geometric meaning of the derivative of a function at a point?
What is the geometric meaning of the derivative of a function at a point?
- The slope of the normal to the curve at the point
- The slope of the curve at the point
- The slope of the chord to the curve at the point
- The slope of the tangent to the curve at the point (correct)
What is the name of the rule that is used to find the derivative of a function when the limit definition is not applicable?
What is the name of the rule that is used to find the derivative of a function when the limit definition is not applicable?
- First principle rule
- Chain rule
- L'Hopital's rule (correct)
- Product rule
What is the application of the derivative of a function at a point?
What is the application of the derivative of a function at a point?
- To find the integral of the function
- To find the rate of change of the function at the point (correct)
- To find the maximum value of the function
- To find the minimum value of the function
What is the notation for the nth derivative of y with respect to x?
What is the notation for the nth derivative of y with respect to x?
What is the derivative of (ax+b)^m with respect to x when m>n?
What is the derivative of (ax+b)^m with respect to x when m>n?
What is the notation for the value of the nth order derivative at x=a?
What is the notation for the value of the nth order derivative at x=a?
What is the derivative of sin(ax+b) with respect to x?
What is the derivative of sin(ax+b) with respect to x?
What is the notation for the nth successive derivative of y?
What is the notation for the nth successive derivative of y?
What is the derivative of the function $f(x) = cos^{-1} (sin x + \frac{x}{2})$ at $x = 1$?
What is the derivative of the function $f(x) = cos^{-1} (sin x + \frac{x}{2})$ at $x = 1$?
If $y = tan^{-1} x$ and $z = sin^{-1} (1 - x^2)$, then what is $\frac{dy}{dx} \div \frac{dz}{dx}$?
If $y = tan^{-1} x$ and $z = sin^{-1} (1 - x^2)$, then what is $\frac{dy}{dx} \div \frac{dz}{dx}$?
What is the value of the limit $\lim_{x \to \infty} \frac{sin^{-1} x}{x}$?
What is the value of the limit $\lim_{x \to \infty} \frac{sin^{-1} x}{x}$?
If $y = tan^{-1} (2x)$, then what is the second derivative of $y$ with respect to $x$?
If $y = tan^{-1} (2x)$, then what is the second derivative of $y$ with respect to $x$?
If y = cos(x + y), what is the derivative of y with respect to x?
If y = cos(x + y), what is the derivative of y with respect to x?
What is the derivative of y = ln(x + y) with respect to x?
What is the derivative of y = ln(x + y) with respect to x?
If y = tan(x + y), what is the derivative of y with respect to x?
If y = tan(x + y), what is the derivative of y with respect to x?
What is the derivative of y = sin(x + y) with respect to x?
What is the derivative of y = sin(x + y) with respect to x?
If y = e^(x + y), what is the derivative of y with respect to x?
If y = e^(x + y), what is the derivative of y with respect to x?
If y = sin⁻¹(x³), then what is y' in terms of x?
If y = sin⁻¹(x³), then what is y' in terms of x?
What is the derivative of cosh(x) with respect to x?
What is the derivative of cosh(x) with respect to x?
If x = sin(θ), then what is dx/dθ in terms of x?
If x = sin(θ), then what is dx/dθ in terms of x?
What is the derivative of tan(x) with respect to x?
What is the derivative of tan(x) with respect to x?
If y = tanh⁻¹(x), then what is y' in terms of x?
If y = tanh⁻¹(x), then what is y' in terms of x?
What is the derivative of $y = sin^{-1} x$ with respect to $x$?
What is the derivative of $y = sin^{-1} x$ with respect to $x$?
If $y = tanh^{-1} x$, then what is the derivative of $y$ with respect to $x$?
If $y = tanh^{-1} x$, then what is the derivative of $y$ with respect to $x$?
What is the derivative of $y = a cos 2x$ with respect to $x$?
What is the derivative of $y = a cos 2x$ with respect to $x$?
What is the derivative of $y = a sin 2x$ with respect to $x$?
What is the derivative of $y = a sin 2x$ with respect to $x$?
If $y = \sinh^{-1} x$, then what is $\frac{dy}{dx}$?
If $y = \sinh^{-1} x$, then what is $\frac{dy}{dx}$?
If $y = \tan^{-1} \left( \frac{2x}{1 - x^2} \right)$, then what is $\frac{dy}{dx}$?
If $y = \tan^{-1} \left( \frac{2x}{1 - x^2} \right)$, then what is $\frac{dy}{dx}$?
If $y = \sin(x^2)$, then what is $\frac{dy}{dx}$?
If $y = \sin(x^2)$, then what is $\frac{dy}{dx}$?
If $y = \cosh^{-1} (2x)$, then what is $\frac{dy}{dx}$?
If $y = \cosh^{-1} (2x)$, then what is $\frac{dy}{dx}$?
