What is the derivative of-e^xsin(y) ?

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int ln^{2} (x + x^{2} + 1) d x

f (x) = \frac{1}{x ^{2}}, (3, \frac{1}{9})

sin^{8} (cos (2 x))

f (x) = sin (x) + x cos (x)

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