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Calculus · Derivatives

Differentiate (r + 1/r)·cos(t)

\frac{d}{dr}\left[\left(r + \frac{1}{r}\right) \cos{\left(t \right)}\right]

Step by step

  1. \frac{d}{dr}\left[\left(r + \frac{1}{r}\right) \cos{\left(t \right)}\right]

    Start from the derivative to compute.

  2. \cos{\left(t \right)} \frac{d}{d r} \left(r + \frac{1}{r}\right)

    Constant multiple rule: pull the constant out.

  3. \left(\frac{d}{d r} \frac{1}{r} + \frac{d}{d r} r\right) \cos{\left(t \right)}

    Sum rule: differentiate term by term.

  4. \left(\frac{d}{d r} \frac{1}{r} + 1\right) \cos{\left(t \right)}

    d/dx of x is 1.

  5. \left(1 - \frac{1}{r^{2}}\right) \cos{\left(t \right)}

    Power rule: (xⁿ)′ = n·xⁿ⁻¹ with n = -1.

Reveal the answer
f'(r) = \left(1 - \frac{1}{r^{2}}\right) \cos{\left(t \right)}