What is the derivative of e^{0.4x}*sin(0.2x) ?

The derivative of e^{0.4x}*sin(0.2x) is e^{0.4x}*0.4sin(0.2x)+cos(0.2x)*0.2e^{0.4x}

What is the first derivative of e^{0.4x}*sin(0.2x) ?

The first derivative of e^{0.4x}*sin(0.2x) is e^{0.4x}*0.4sin(0.2x)+cos(0.2x)*0.2e^{0.4x}

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\frac{d}{d x} (e^{0.4 x} \cdot sin (0.2 x))

e^{0.4 x} \cdot 0.4 sin (0.2 x) + cos (0.2 x) \cdot 0.2 e^{0.4 x}

Solution steps

\frac{d}{d x} (e^{0.4 x} sin (0.2 x))

Apply the Product Rule:

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

f = e^{0.4 x}, g = sin (0.2 x)

= \frac{d}{d x} (e^{0.4 x}) sin (0.2 x) + \frac{d}{d x} (sin (0.2 x)) e^{0.4 x}

\frac{d}{d x} (e^{0.4 x}) = e^{0.4 x} \cdot 0.4

\frac{d}{d x} (sin (0.2 x)) = cos (0.2 x) \cdot 0.2

= e^{0.4 x} \cdot 0.4 sin (0.2 x) + cos (0.2 x) \cdot 0.2 e^{0.4 x}

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

\int \frac{1}{16 + 9 x ^{2}} d x

\frac{17}{x}

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

y^{^{''}} + 3 (y^{^{'}})^{2} = - 17

What is the derivative of e^{0.4x}*sin(0.2x) ?
The derivative of e^{0.4x}*sin(0.2x) is e^{0.4x}*0.4sin(0.2x)+cos(0.2x)*0.2e^{0.4x}
What is the first derivative of e^{0.4x}*sin(0.2x) ?
The first derivative of e^{0.4x}*sin(0.2x) is e^{0.4x}*0.4sin(0.2x)+cos(0.2x)*0.2e^{0.4x}