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

The derivative of (e^xsin(x)) is e^xsin(x)+cos(x)e^x

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

The first derivative of (e^xsin(x)) is e^xsin(x)+cos(x)e^x

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

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

Solution steps

\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}

(\frac{1}{x - 1})^{^{'}}

t cos (3 t) + 2 e^{- 4 t}

\int e^{- 3 x} sin (5 x) d x

\frac{d}{d x} (\frac{c ^{9} - x ^{9}}{c ^{9} + x ^{9}})

\int (\frac{1}{x ^{1.2}}) d x

What is the derivative of (e^xsin(x)) ?
The derivative of (e^xsin(x)) is e^xsin(x)+cos(x)e^x
What is the first derivative of (e^xsin(x)) ?
The first derivative of (e^xsin(x)) is e^xsin(x)+cos(x)e^x