Calculus • Step-by-Step

Derivative of 3x² + 5x - 4 with Steps

Differentiate the polynomial 3x² + 5x - 4 term by term using power, linear, and constant rules to find 6x + 5.

Problem Statement

\frac{d}{dx}[3x^2 + 5x - 4]

Final Result

f'(x) = 6 \cdot x+5

Formula Required: Sum & Constant Multiple Rule

Differentiate each term independently and sum the results.

\frac{d}{dx}[a x^2 + b x + c] = 2ax + b

6 Steps

Set up the differentiation problem with respect to variable $x$.

\frac{d}{dx} \left[ 3 \cdot x^{2}+5 \cdot x-4 \right]

Apply the Sum & Difference Rule: differentiate each term separately.

\frac{d}{dx} \left[ 3 \cdot x^{2}+5 \cdot x-4 \right] = \frac{d}{dx}\left[ 3 \cdot x^{2} \right] + \frac{d}{dx}\left[ 5 \cdot x \right] - \frac{d}{dx}\left[ -4 \right]

Differentiate $3 \cdot x^{2}$ using the Power Rule.

\frac{d}{dx}\left[ 3 \cdot x^{2} \right] = 6 \cdot x

The derivative of linear term $5 \cdot x$ is its coefficient.

\frac{d}{dx}\left[ 5 \cdot x \right] = 5

The derivative of constant $4$ is $0$.

\frac{d}{dx}\left[ 4 \right] = 0

Combine all term derivatives and simplify algebraic terms.

\frac{d}{dx}\left[ 3 \cdot x^{2}+5 \cdot x-4 \right] = 6 \cdot x+5

Interactive Calculator

Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.

Apply the power rule to each term: d/dx[3x²] = 6x, d/dx[5x] = 5, and d/dx[-4] = 0. Adding them gives 6x + 5.