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人気のある微分積分 >

derivative of e^{ax}sin(bx)

解

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

解

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

解答ステップ

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

積の法則を適用:

(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}

人気の例

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

d er i v a t i v e \frac{x - 13}{x - 13}

(6x+1)y^2(dy)/(dx)+4x^2+2y^3=0

(6 x + 1) y^{2} \frac{d y}{d x} + 4 x^{2} + 2 y^{3} = 0