Question

Find the derivatives of the following function with respect to x and simplify the result. y=e^{x}\sin h x

Derivatives
ANSWERED
asked 2021-05-08
Find the derivatives of the following function with respect to x and simplify the result.
\(\displaystyle{y}={e}^{{{x}}}{\sin{{h}}}{x}\)

Answers (1)

2021-05-09

Step 1
\(\displaystyle{y}={e}^{{{x}}}{\sin{{h}}}{\left({x}\right)}\)
Apply product rule for taking derivative
\(y=uv\)
\(y'=u'v+v'(u)\)
derivative of \(\displaystyle{\sin{{h}}}{\left({x}\right)}\ {i}{s}\ {\cos{{h}}}{\left({x}\right)}\)
Step 2
\(\displaystyle{y}={e}^{{{x}}}{\sin{{h}}}{\left({x}\right)}\)
\(\displaystyle{y}'={e}^{{{x}}}{\sin{{h}}}{\left({x}\right)}+{e}^{{{x}}}{\cos{{h}}}{\left({x}\right)}\)
\(\displaystyle{y}'={e}^{{{x}}}{\left({\sin{{h}}}{\left({x}\right)}+{\cos{{h}}}{\left({x}\right)}\right)}\)

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