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

The derivative of-e^xsin(x) is -e^xsin(x)-e^xcos(x)

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

The first derivative of-e^xsin(x) is -e^xsin(x)-e^xcos(x)

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

- e^{x} sin (x) - e^{x} cos (x)

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

= - (e^{x} sin (x) + cos (x) e^{x})

Simplify

- (e^{x} sin (x) + cos (x) e^{x}) : - e^{x} sin (x) - e^{x} cos (x)

= - e^{x} sin (x) - e^{x} cos (x)

\frac{d}{d x} (x^{2} + h^{2})

\int (e^{2 x} - e^{- 2 x}) d x

\int 100 - x^{2} d x

\int_{- 1}^{1} 4 d x

\frac{\partial}{\partial x} (ln (6 x^{2} + 7 y^{2} + 7))

What is the derivative of-e^xsin(x) ?
The derivative of-e^xsin(x) is -e^xsin(x)-e^xcos(x)
What is the first derivative of-e^xsin(x) ?
The first derivative of-e^xsin(x) is -e^xsin(x)-e^xcos(x)