A comprehensive quiz on differentiation techniques including first principles, product, quotient, and chain rules, as well as implicit and parametric…
10 questions • Zestly
• Using the definition of the derivative from first principles, $f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$, determine the derivative of…
• Identify which of the following functions have a derivative equal to themselves, i.e., $f'(x) = f(x)$.
• If $y = x^2 \sin(x)$, what is the derivative $\frac{dy}{dx}$?
• Given $y = \sin(x^3)$, find $\frac{dy}{dx}$ using the chain rule.
• For the implicit equation $x^2 + y^2 = 25$, what is the expression for $\frac{dy}{dx}$?
• A curve is defined parametrically by $x = t^2$ and $y = t^3$. What is $\frac{dy}{dx}$ in terms of $t$?
• Which of the following statements are true regarding the derivatives of trigonometric functions?
• If $y = e^{2x}$, what is the second derivative $\frac{d^2y}{dx^2}$?
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