Use the rule 𝑑 𝑑𝑥 𝑥𝑛 = 𝑛𝑥𝑛−1 for positive integers.

Find the derivative of $f(x) = 5x^4 - 3x^2 + 7x - 2$ using the power rule.

Find the derivative of $f(x) = 5x^4 - 3x^2 + 7$.

A company's total production cost, in dollars, is modelled by the function \(C(x) = 2{,}400 + 15x + 0.2x^3\), where \(x\) is the number of units produced per day and \(0 \le x \le 50\). (a) Use the differentiation rule to determine the marginal cost function \(C'(x)\). (2 marks) (b) Use your result from part (a) to calculate the marginal cost when 20 units are produced per day. Give your answer in dollars. (2 marks)

A function is defined as $f(x) = 5x^4 - 3x^2 + 7$. (a) Use the power rule to find $f'(x)$. [1 mark] (b) Hence evaluate $f'(2)$. [1 mark] (c) Determine the value of $f'(1) + f'(-1)$. [1 mark]