What is the derivative of e^xcos(y) ?

The derivative of e^xcos(y) is e^xcos(y)-e^xsin(y)(dy)/(dx)

What is the first derivative of e^xcos(y) ?

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

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = cos (y)

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

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

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

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

Simplify

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

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