Derivative of \( \displaystyle - \cos{\left(5 x - 1 \right)} \)

Problem 2.596 · easy

1. \[ \frac{d}{d x} \left(- \cos{\left(5 x - 1 \right)}\right) \]
   Start with the derivative of the function.✓ Proved
2. \[ = - \frac{d}{d x} \cos{\left(5 x - 1 \right)} \]
   constantPull the constant -1 out of the derivative.✓ Proved
3. \[ = \sin{\left(5 x - 1 \right)} \frac{d}{d x} \left(5 x - 1\right) \]
   trig algebraApply the derivative rule for cosine. Simplify the signs.✓ Proved
4. \[ = \left(- \frac{d}{d x} 1 + \frac{d}{d x} 5 x\right) \sin{\left(5 x - 1 \right)} \]
   sumSplit the derivative of the inner function.✓ Proved
5. \[ = \sin{\left(5 x - 1 \right)} \frac{d}{d x} 5 x \]
   constant algebraThe derivative of a constant is zero. Simplify the expression.✓ Proved
6. \[ = 5 \sin{\left(5 x - 1 \right)} \]
   derivative algebraDifferentiate the linear term 5*x. Final simplified form.✓ Proved