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If y = (x2+3x−1)(2x−5), find racdydx.

May 20, 2026Mathematics

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Graph of y = (x² + 3x − 1)(2x − 5)

Step-by-step solution

3 steps

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1. CALCULUS (DIFFERENTIATION & INTEGRATION)

a) If $y = (x^2+3x-1)(2x-5)$ , find $\frac{dy}{dx}$ .

Apply the product rule $\frac{dy}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}$ .
Let $u = x^2+3x-1$ and $v = 2x-5$ .
Then $\frac{du}{dx} = 2x+3$ and $\frac{dv}{dx} = 2$ .
Substitute into the product rule formula.
$\frac{dy}{dx} = (x^2+3x-1)(2) + (2x-5)(2x+3)$
Expand and simplify.
$\frac{dy}{dx} = 2x^2+6x-2 + (4x^2+6x-10x-15)$ $\frac{dy}{dx} = 2x^2+6x-2 + 4x^2-4x-15$ $\frac{dy}{dx} = 6x^2+2x-17$
The derivative is $\boxed{