Daily Math · 2026-07-08

Question 1

The derivative of $f(x) = x^3 \sin x$ is:

Accepted Answer

By the product rule, $f'(x) = (x^3)'\sin x + x^3(\sin x)' = 3x^2 \sin x + x^3 \cos x$.

Answer

$3x^2 \sin x + x^3 \cos x$

Answer

$3x^2 \cos x$

Answer

$x^3 \cos x$

Answer

$3x^2 \sin x - x^3 \cos x$

Question 2

The value of $\cos 36^\circ - \cos 72^\circ$ is:

Accepted Answer

Using the closed forms $\cos 36^\circ = 	frac{1+\sqrt{5}}{4}$ and $\cos 72^\circ = 	frac{\sqrt{5}-1}{4}$, the difference is $	frac{(1+\sqrt{5}) - (\sqrt{5}-1)}{4} = 	frac{2}{4} = 	frac{1}{2}$.

Answer

$	frac{1}{2}$

Answer

$	frac{\sqrt{5}}{4}$

Answer

$	frac{1}{4}$

Answer

$1$

Question 3

A linear regression of test score $y$ on hours studied $x$ gives $\hat{y} = 50 + 8x$. By how much does the predicted score increase when $x$ increases by $0.5$?

Accepted Answer

The slope is $8$ score points per additional hour. For a $0.5$-hour increase, the predicted change is $0.5 	imes 8 = 4$.

Answer

$0.5$

Answer

$4$

Answer

$8$

Answer

$54$

Problems & worked solutions

Problem 1 — Calculus

Problem 2 — Trigonometry

Problem 3 — Linear Regression Interpretation