What is the derivative of sin(xe^x) ?

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

What is the first derivative of sin(xe^x) ?

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\int \frac{1}{2 x ( x - 1 )} d x

5 x^{3}

\int x sin^{2} (3 x) d x

\int 3 t d t

1 - x x

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