Derivative of Function of Constant Multiple/Examples/Cosine of a x + b
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Example of Derivative of Function of Constant Multiple
- $\map {\dfrac \d {\d x} } {\map \cos {a x + b} } = -a \map \sin {a x + b}$
Proof
| \(\ds \map {\dfrac \d {\d x} } {\map \cos {a x + b} }\) | \(=\) | \(\ds a \map {\dfrac \d {\map \d {a x + b} } } {\map \cos {a x + b} }\) | Derivative of Function of Constant Multiple: Corollary | |||||||||||
| \(\ds \) | \(=\) | \(\ds -a \map \sin {a x + b}\) | Derivative of Cosine Function |
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text {II}$. Calculus: Differentiation: Exercises $\text {IX}$: $9$.