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Calculus · Derivatives

Differentiate cos(sin(x))

\frac{d}{dx}\left[\cos{\left(\sin{\left(x \right)} \right)}\right]

Step by step

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

    Start from the derivative to compute.

  2. - \sin{\left(\sin{\left(x \right)} \right)} \frac{d}{d x} \sin{\left(x \right)}

    Chain rule: (cos u)′ = −sin u, times u′ where u = \sin{\left(x \right)}.

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

    (sin u)′ = cos u.

Reveal the answer
f'(x) = - \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}