![y=(\sin(7x))^{\ln(x) } \\ \\ \ln{y}=\ln[(\sin(7x))^{\ln(x) }] \\ \\ \ln{y}=\ln(x)\ln[(\sin(7x))] \\ \\ (\ln{y})'=(\ln(x)\ln[(\sin(7x))])' \\ \\ \frac{1}{y} dy=[\frac{1}x}\ ln \sin(7x) +\frac{7 \cos (7x)}{sin(7x)}\ln{x}] dx \\ \\ \frac{dy}{dx} =y[\frac{1}x}\ ln \sin(7x) +\frac{7 \cos (7x)}{sin(7x)}\ln{x}] \\ \\ \frac{dy}{dx} =(\sin(7x))^{\ln(x) }[\frac{1}x}\ ln \sin(7x) +\frac{7 \cos (7x)}{sin(7x)}\ln{x}]](/tpl/images/0257/9457/c7519.png)
y=(sin(7x))^ln(x)
Mathematics, 24.09.2019 10:50 Yommms
Use logarithmic differentiation to find the derivative of the function.
y=(sin(7x))^ln(x)
y'=?
Answers: 1
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You know the right answer?
Use logarithmic differentiation to find the derivative of the function.
y=(sin(7x))^ln(x)
y=(sin(7x))^ln(x)
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