What is the derivative of e^{ax}sin(bx) ?

The derivative of e^{ax}sin(bx) is e^{ax}asin(bx)+cos(bx)be^{ax}

What is the first derivative of e^{ax}sin(bx) ?

The first derivative of e^{ax}sin(bx) is e^{ax}asin(bx)+cos(bx)be^{ax}

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derivative of

e^{a x} sin (b x)

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

x \to 3 lim (e^{\frac{2}{3 - x}})

\frac{\partial}{\partial y} (e^{2 x} cos (y))

\int e^{- x} cos^{2} (x) d x

\int (x 9 - x^{2}) d x

\frac{d y}{d x} = e^{2 y + 2 x}

What is the derivative of e^{ax}sin(bx) ?
The derivative of e^{ax}sin(bx) is e^{ax}asin(bx)+cos(bx)be^{ax}
What is the first derivative of e^{ax}sin(bx) ?
The first derivative of e^{ax}sin(bx) is e^{ax}asin(bx)+cos(bx)be^{ax}