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Find the derivative of \( y \) with respect ...
Solve them please
Find the derivative of \( y \) with respect to \( x \). \[ y=e\left(4 \sqrt{x}+x^{6}\right) \] A. \( \left(\frac{2}{\sqrt{x}}+6 x^{5}\right) e^{\left(4 \sqrt{x}+x^{6}\right)} \) B. \( e^{\left(2 \sqrt{x}+6 x^{5}\right)} \) C. \( \left.4 \sqrt{x}+6 x^{5}\right) e\left(4 \sqrt{x}+x^{6}\right) \) D. \( \left(4 \sqrt{x}+6 x^{5}\right) \ln \left(4 \sqrt{x}+x^{6}\right) \)
Find the derivative of \( y \) with respect to \( t \). \[ y=e^{\sin t}\left(\ln t^{4}+6\right) \] A. \( e^{\sin t}\left(\ln t^{4}+6+\frac{4}{t}\right) \) B. \( e^{\sin t}\left((\cos t)\left(\ln t^{4}+6\right)+\frac{4}{t}\right) \) C. \( e^{\cos t}(\cos t)\left(\ln t^{4}+6\right)+\frac{4 e^{\sin t}}{t} \) D. \( \frac{4 e^{\sin t} \cos t}{t} \)
\( \frac{d y}{d x} \) \( 8 x y=e^{x+y} \) A. \( \frac{2 x y e^{x+y}}{x+y} \) B. \( \frac{e^{x+y}}{e^{8 x}} \) C. \( \frac{y}{x} \) D. \( \frac{x y e^{x+y}-y}{x-x y e^{x+y}} \)
Find the derivative of \( y \) with respect to the independent variable. \( y=8^{\cos \pi \theta} \) A. \( 8^{\cos \pi \theta} \) B. \( \pi 8^{\cos \pi \theta} \ln 8 \) C. \( -\pi 8^{\cos \pi \theta} \ln 8 \sin \pi \theta \) D. \( -8^{\cos \pi \theta} \ln 8 \sin \pi \theta \)