What is the derivative of axcos(x+bxsin(x)) ?

The derivative of axcos(x+bxsin(x)) is a(cos(x)-xsin(x))+b(sin(x)+xcos(x))

What is the first derivative of axcos(x+bxsin(x)) ?

The first derivative of axcos(x+bxsin(x)) is a(cos(x)-xsin(x))+b(sin(x)+xcos(x))

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

a (cos (x) - x sin (x)) + b (sin (x) + x cos (x))

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= a (cos (x) - x sin (x)) + b (sin (x) + x cos (x))

What is the derivative of axcos(x+bxsin(x)) ?
The derivative of axcos(x+bxsin(x)) is a(cos(x)-xsin(x))+b(sin(x)+xcos(x))
What is the first derivative of axcos(x+bxsin(x)) ?
The first derivative of axcos(x+bxsin(x)) is a(cos(x)-xsin(x))+b(sin(x)+xcos(x))