MAT 112 - Differentiation - QUIZ

MAT 112 · Differentiation

University of Fort Hare

Practice 10 questions on MAT 112 - Differentiation at University of Fort Hare. Free AI-generated quiz on uNotes — track your score, retake anytime.

Questions

1Using the First Principle (definition of derivatives), determine the derivative of $f(x) = \sqrt{3 - 2x}$.

2Find the equation of the line perpendicular to the tangent to the curve $y = x^3 - 3x + 1$ at the point (2, 3).

3Using the product rule and chain rule, find the derivative $\frac{dy}{dx}$ of the function $y = xe^{2x}$.

4What is the derivative of $y = x^x$ using logarithmic differentiation?

5Given the implicit equation $\sqrt{x} + \sqrt{y} = 4$, which of the following expressions represent $\frac{dy}{dx}$? Select all that apply.

6If $f(x) = \frac{1}{(2x - 1)^5}$, calculate the value of the second derivative at $x = 0$, i.e., $f''(0)$.

7Find the derivative of the inverse trigonometric function $y = \tan^{-1}(\ln x)$.

8In the binomial expansion of $(\frac{1}{x} - x^2)^{12}$, find the middle term.

9Suppose that $f(5)=1$, $f'(5)=6$, $g(5)=-3$, and $g'(5)=2$. Find the value of $\frac{d}{dx}[\frac{f(x)}{g(x)}]$ at $x=5$.

10Identify the correct expressions for the derivative of $y = \sin(3x)\cos(5x)$. Select all that apply.