What is the derivative of x3 + 2x?

Mathematics

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nx^{n-1},weget, we get \frac{d}{dx}(x^3) = 3x^{3-1} = 3x^2$.

The derivative of x3+2xx^3 + 2x is 3x2+23x^2 + 2.

Steps: To find the derivative, we apply the sum rule and the power rule for differentiation:

  1. Derivative of x3x^3: Using the power rule ddx(xn)=nxn−1\frac{d}{dx}(x^n) = nx^{n-1}, we get ddx(x3)=3x3−1=3x2\frac{d}{dx}(x^3) = 3x^{3-1} = 3x^2.
  2. Derivative of 2x2x: Using the constant multiple rule and the power rule, we get ddx(2x)=2⋅ddx(x1)=2⋅1x1−1=2⋅1x0=2⋅1=2\frac{d}{dx}(2x) = 2 \cdot \frac{d}{dx}(x^1) = 2 \cdot 1x^{1-1} = 2 \cdot 1x^0 = 2 \cdot 1 = 2.
  3. Sum the derivatives: ddx(x3+2x)=ddx(x3)+ddx(2x)=3x2+2\frac{d}{dx}(x^3 + 2x) = \frac{d}{dx}(x^3) + \frac{d}{dx}(2x) = 3x^2 + 2.
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The derivative of x^3 + 2x is 3x^2 + 2. Steps: To find the derivative, we apply the sum rule and the power rule for differentiation: 1.

What is the derivative of x3 + 2x?
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
The derivative of x^3 + 2x is 3x^2 + 2. Steps: To find the derivative, we apply the sum rule and the power rule for differentiation: 1. Derivative of x^3: Using the power rule (d)/(dx)(x^n) = nx^n-1, we get (d)/(dx)(x^3) = 3x^3-1 = 3x^2. 2. Derivative of 2x: Using the constant multiple rule and the power rule, we get (d)/(dx)(2x) = 2 · (d)/(dx)(x^1) = 2 · 1x^1-1 = 2 · 1x^0 = 2 · 1 = 2. 3. Sum the derivatives: (d)/(dx)(x^3 + 2x) = (d)/(dx)(x^3) + (d)/(dx)(2x) = 3x^2 + 2.