Question

Derivative of 14/(cos0.5x)

Answer 1

\[\large \frac{ 14 }{ \cos(\frac{ 1 }{ 2 }x) }\]Do you remember cosine's relationship to secant? :D
\[\large = 14\sec(\frac{ 1 }{ 2 }x)\]

Do you know the derivative of secant? If not, we can go back to the start and work with the cosine.

Answer 2

Work from start

Answer 3

\[\large \frac{ 14 }{ \cos(\frac{ 1 }{ 2 }x) }=14[\cos(\frac{ 1 }{ 2 }x)]^{-1}\]
So I guess we can bring the cosine up, applying a negative exponent to it. (Be careful not to confuse it with the inverse cosine, that's why I wrote it on the outside instead :D ).

From here, we can take the derivative of the OUTERMOST function first (the -1 power). Then apply the chain rule, multiplying by the derivative of the inside.

Understand how to do that? :D

Answer 4

Yes