Solved: Find the derivative $\frac{dy}{dx}$ of the algebraic function: $y = 3x^3 - 5x^2 + 2x - 7$.

Question

Find the derivative $\frac{dy}{dx}$ of the algebraic function: $y = 3x^3 - 5x^2 + 2x - 7$ .

Verified Answer

$9x^2 - 10x + 2$

Explanation & Step-by-Step Solving

Context: Apply the basic power rule of differentiation $\frac{d}{dx}(ax^n) = anx^{n-1}$ term by term: $\frac{dy}{dx} = (3 \times 3)x^{3-1} - (5 \times 2)x^{2-1} + 2 = 9x^2 - 10x + 2$

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