What is the derivative of ae^xcos(x+be^xsin(x)) ?

The derivative of ae^xcos(x+be^xsin(x)) is a(e^xcos(x)-e^xsin(x))+b(e^xsin(x)+cos(x)e^x)

What is the first derivative of ae^xcos(x+be^xsin(x)) ?

The first derivative of ae^xcos(x+be^xsin(x)) is a(e^xcos(x)-e^xsin(x))+b(e^xsin(x)+cos(x)e^x)

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

\int \frac{14 x ^{2} + 9 x + 43}{( x + 2 ) ( x ^{2} + 5 )} d x

\int + sin^{2} (6 x) cos^{2} (6 x) d x

\int [\frac{1}{x ^{2}} + sec^{2} (π x)] d x

\frac{\partial}{\partial x} ((x y)^{\frac{1}{2}})

What is the derivative of ae^xcos(x+be^xsin(x)) ?
The derivative of ae^xcos(x+be^xsin(x)) is a(e^xcos(x)-e^xsin(x))+b(e^xsin(x)+cos(x)e^x)
What is the first derivative of ae^xcos(x+be^xsin(x)) ?
The first derivative of ae^xcos(x+be^xsin(x)) is a(e^xcos(x)-e^xsin(x))+b(e^xsin(x)+cos(x)e^x)