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Calculus · Derivatives

Differentiate -sin(3t - x)

\frac{d}{dx}\left[- \sin{\left(3 t - x \right)}\right]

Step by step

  1. \frac{d}{dx}\left[- \sin{\left(3 t - x \right)}\right]

    Start from the derivative to compute.

  2. - \frac{\partial}{\partial x} \sin{\left(3 t - x \right)}

    Constant multiple rule: pull the constant out.

  3. - \cos{\left(3 t - x \right)} \frac{\partial}{\partial x} \left(3 t - x\right)

    Chain rule: (sin u)′ = cos u, times u′ where u = 3 t - x.

  4. - \left(\frac{d}{d x} 3 t + \frac{d}{d x} \left(- x\right)\right) \cos{\left(3 t - x \right)}

    Sum rule: differentiate term by term.

  5. - \left(\frac{d}{d x} 3 t - \frac{d}{d x} x\right) \cos{\left(3 t - x \right)}

    Constant multiple rule: pull the constant out.

  6. - \left(\frac{d}{d x} 3 t - 1\right) \cos{\left(3 t - x \right)}

    d/dx of x is 1.

  7. \cos{\left(3 t - x \right)}

    The derivative of a constant is 0.

Reveal the answer
f'(x) = \cos{\left(3 t - x \right)}