What is the derivative of 0.09e^xsin(x) ?

The derivative of 0.09e^xsin(x) is 0.09(e^xsin(x)+cos(x)e^x)

What is the first derivative of 0.09e^xsin(x) ?

The first derivative of 0.09e^xsin(x) is 0.09(e^xsin(x)+cos(x)e^x)

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derivative of

0.09 e^{x} sin (x)

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

Solution steps

\frac{d}{d x} (0.09 e^{x} sin (x))

Take the constant out:

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

= 0.09 \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)

= 0.09 (\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)

= 0.09 (e^{x} sin (x) + cos (x) e^{x})

What is the derivative of 0.09e^xsin(x) ?
The derivative of 0.09e^xsin(x) is 0.09(e^xsin(x)+cos(x)e^x)
What is the first derivative of 0.09e^xsin(x) ?
The first derivative of 0.09e^xsin(x) is 0.09(e^xsin(x)+cos(x)e^x)