What is the derivative of e^xcos(y+ln(x^2y)) ?

The derivative of e^xcos(y+ln(x^2y)) is e^xcos(y)-e^xsin(y)(dy)/(dx)+(2y+x\frac{dy)/(dx)}{xy}

What is the first derivative of e^xcos(y+ln(x^2y)) ?

The first derivative of e^xcos(y+ln(x^2y)) is e^xcos(y)-e^xsin(y)(dy)/(dx)+(2y+x\frac{dy)/(dx)}{xy}

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\frac{d}{d x} (e^{x} cos (y) + ln (x^{2} y))

e^{x} cos (y) - e^{x} sin (y) \frac{d y}{d x} + \frac{2 y + x \frac{d y}{d x}}{x y}

Solution steps

\frac{d}{d x} (e^{x} cos (y) + ln (x^{2} y))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (e^{x} cos (y)) + \frac{d}{d x} (ln (x^{2} y))

\frac{d}{d x} (e^{x} cos (y)) = e^{x} cos (y) - e^{x} sin (y) \frac{d y}{d x}

\frac{d}{d x} (ln (x^{2} y)) = \frac{2 y + x \frac{d y}{d x}}{x y}

= e^{x} cos (y) - e^{x} sin (y) \frac{d y}{d x} + \frac{2 y + x \frac{d y}{d x}}{x y}

e^{x} - x^{6}

\frac{1}{9 s}

\frac{d v}{d t} = \frac{457.8 - 7 v}{2180}

y^{^{'}} = 2 y + x^{2} e^{2 x}

e^{- 3 x} (y + 1) d y = x e^{3 x} (1 + y^{3}) d x

What is the derivative of e^xcos(y+ln(x^2y)) ?
The derivative of e^xcos(y+ln(x^2y)) is e^xcos(y)-e^xsin(y)(dy)/(dx)+(2y+x\frac{dy)/(dx)}{xy}
What is the first derivative of e^xcos(y+ln(x^2y)) ?
The first derivative of e^xcos(y+ln(x^2y)) is e^xcos(y)-e^xsin(y)(dy)/(dx)+(2y+x\frac{dy)/(dx)}{xy}