Question

Find the derivatives of the following function with respect to x and simplify the result. y=\cos h(\log x)

Derivatives
ANSWERED
asked 2021-05-25
Find the derivatives of the following function with respect to x and simplify the result.
\(\displaystyle{y}={\cos{{h}}}{\left({\log{{x}}}\right)}\)

Answers (1)

2021-05-26
Step 1
To find the derivative of hyperbolic function with respect to x
Use chain rule
Step 2
\(\displaystyle{y}={\cos{{h}}}{\left({\log{{x}}}\right)}\)
\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left({\cos{{h}}}{\left({\log{{x}}}\right)}\right)}\)
\(\displaystyle={\sin{{h}}}{\left({\log{{x}}}\right)}\cdot{\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left({\log{{x}}}\right)}\)
\(\displaystyle={\sin{{h}}}{\left({\log{{x}}}\right)}\cdot{\left({\frac{{{1}}}{{{x}}}}\right)}\)
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