en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of e^{ax}sin(bx)

Solution

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

Solution

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}

Popular Examples

x^2(dy)/(dx)=1-x^2+y^2-x^2y^2

x^{2} \frac{d y}{d x} = 1 - x^{2} + y^{2} - x^{2} y^{2}

integral of (x-a)^2

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

integral of (x^2+1)/((x^2-2x+2)^2)

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

derivative of (x-13)/(sqrt(x)-\sqrt{13)}derivative of

\frac{x - 13}{x - 13}

integral from-5 to 5 of 1/2 (25-x^2)

\int_{- 5}^{5} \frac{1}{2} (25 - x^{2}) d x

Frequently Asked Questions (FAQ)

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}