What is the derivative of e^x(acos(x+bsin(x))) ?

The derivative of e^x(acos(x+bsin(x))) is e^x(acos(x)+bsin(x))+(-asin(x)+bcos(x))e^x

What is the first derivative of e^x(acos(x+bsin(x))) ?

The first derivative of e^x(acos(x+bsin(x))) is e^x(acos(x)+bsin(x))+(-asin(x)+bcos(x))e^x

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\int x^{6} e^{- x^{7}} d x

y = x^{2} - 4 x + 3, (1, 0)

\frac{d}{d x} (\frac{x ( 1 + z ( x ) )}{1 - z ( x )})

\frac{d y}{d x} = 5 x e^{6 y}

3 x + 18, x^{2}

What is the derivative of e^x(acos(x+bsin(x))) ?
The derivative of e^x(acos(x+bsin(x))) is e^x(acos(x)+bsin(x))+(-asin(x)+bcos(x))e^x
What is the first derivative of e^x(acos(x+bsin(x))) ?
The first derivative of e^x(acos(x+bsin(x))) is e^x(acos(x)+bsin(x))+(-asin(x)+bcos(x))e^x