Derivative of \( \displaystyle 5 x \left(5 x + 4\right) \)

Problem 2.697 · medium

1. \[ \frac{d}{d x} 5 x \left(5 x + 4\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(25 x^{2} + 20 x\right) \]
   algebraExpand the expression using distributive property.✓ Proved
3. \[ = \frac{d}{d x} 20 x + \frac{d}{d x} 25 x^{2} \]
   sumApply the sum rule for derivatives.✓ Proved
4. \[ = 20 \frac{d}{d x} x + 25 \frac{d}{d x} x^{2} \]
   constant-multipleFactor out the constants.✓ Proved
5. \[ = 50 x + 20 \]
   power algebraApply the power rule to each term. Simplify the coefficients.✓ Proved