What is the derivative of xcos(y-ye^x) ?

The derivative of xcos(y-ye^x) is cos(y)-xsin(y)(dy)/(dx)-e^x(dy)/(dx)-e^xy

What is the first derivative of xcos(y-ye^x) ?

The first derivative of xcos(y-ye^x) is cos(y)-xsin(y)(dy)/(dx)-e^x(dy)/(dx)-e^xy

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

x \to 5 lim (\frac{x ^{2} - 7 x + 10}{x ^{2} - 25})

\frac{d y}{d x} = \frac{2 y + x ^{2} - y ^{2}}{2 x}

\int \frac{sec ^{6} ( x )}{tan ^{3} ( x )} d x

x \to 0 - lim (e^{\frac{3}{x}})

x \to 0 lim (\frac{x + 5}{3 x})

What is the derivative of xcos(y-ye^x) ?
The derivative of xcos(y-ye^x) is cos(y)-xsin(y)(dy)/(dx)-e^x(dy)/(dx)-e^xy
What is the first derivative of xcos(y-ye^x) ?
The first derivative of xcos(y-ye^x) is cos(y)-xsin(y)(dy)/(dx)-e^x(dy)/(dx)-e^xy