Solve this differentiation question y = 5x ^ 2 + 2x + 5

April 26, 2026Mathematics

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Answer

\frac{dy}{dx} = 10x + 2

Graph of y = 5x² + 2x + 5

Key points of y = 5x² + 2x + 5
Point	x	y
Minimum	−0.2	4.8
y-intercept	0	5

Step-by-step solution

2 steps

To differentiate $y = 5x^2 + 2x + 5$ , we will use the power rule for differentiation, which states that $\frac{d}{dx}(ax^n) = nax^{n-1}$ , and the rule that the derivative of a constant is zero.

Differentiate each term with respect to $x$ .
For the first term, $5x^2$ :
$\frac{d}{dx}(5x^2) = 2 \cdot 5x^{2-1} = 10x^1 = 10x$
For the second term, $2x$ :
$\frac{d}{dx}(2x) = 1 \cdot 2x^{1-1} = 2x^0 = 2 \cdot 1 = 2$
For the third term, 5 (a constant):
$\frac{d}{dx}(5) = 0$
Combine the derivatives of each term.
$\frac{dy}{dx} = 10x + 2 + 0$ $\frac{dy}{dx} = 10x + 2$
The derivative of $y = 5x^2 + 2x + 5$ is:

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