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Asher Kaufman

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2022-08-19

Find the derivative. Simplify where possible.

y = \sin h (\cos h x)

Answer & Explanation

Leon Clark

Beginner2022-08-20Added 9 answers

y = \sin h (\cos h x)

Differentiate

\frac{d y}{d x} = \frac{d [\sin h (\cos h x)]}{d x}

Use Chain Rule

\frac{d y}{d x} = \frac{d [\sin h (\cos h x)]}{d (\cos h x)} \times \frac{d (\cos h x)}{d x}

Recall that:

\frac{d (\sin h x)}{d x} = \cos h x \frac{d (\cos h x)}{d x} = \sin h x

\frac{d y}{d x} = \frac{d [\sin h (\cos h x)]}{d (\cos h x)} \times \frac{d (\cos h x)}{d x}

\frac{d y}{d x} = \cos h (\cos h x) \times (\sin h x)

\frac{d y}{d x} = \sin h x \cdot \cos h (\cos h x)

Result:

\frac{d y}{d x} = \sin h x \cdot \cos h (\cos h x)

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