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Differentiate: y = x3 + 4x − 3.

June 3, 2026Mathematics

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Answer

\frac{dy}{dx} = 3x^2 + 4

Graph of y = x³ + 4x − 3

Key points of y = x³ + 4x − 3
Point	x	y
y-intercept	0	−3
x-intercept	0.67	0

2 steps

b) Differentiate: $y = x^3 + 4x - 3$ .

Apply the power rule for differentiation, $\frac{d}{dx}(x^n) = nx^{n-1}$ , to each term.
For $x^3$ , the derivative is $3x^{3-1} = 3x^2$ .
For $4x$ , the derivative is $4x^{1-1} = 4x^0 = 4$ .
For the constant term $-3$ , the derivative is 0.
Combine the derivatives of each term to find $\frac{dy}{dx}$ .
$\frac{dy}{dx} = 3x^2 + 4 - 0$ $\frac{dy}{dx} = \boxed{3x^2 + 4}$

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