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Calculus · Derivatives

Differentiate -sin(3t - x)

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

Step by step

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

    Start from the derivative to compute.

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

    Constant multiple rule: pull the constant out.

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

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

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

    Sum rule: differentiate term by term.

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

    The derivative of a constant is 0.

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

    Constant multiple rule: pull the constant out.

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

    d/dx of x is 1.

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