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Popular >

derivative of 2e^xsin(x)

Solution

\frac{d}{d x} (2 e^{x} sin (x))

Solution

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

Solution steps

\frac{d}{d x} (2 e^{x} sin (x))

Take the constant out:

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

= 2 \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)

= 2 (\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)

= 2 (e^{x} sin (x) + cos (x) e^{x})

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 2e^xsin(x) ?
The derivative of 2e^xsin(x) is 2(e^xsin(x)+cos(x)e^x)
What is the first derivative of 2e^xsin(x) ?
The first derivative of 2e^xsin(x) is 2(e^xsin(x)+cos(x)e^x)