What is the derivative of axcos(3x+bxsin(3x)) ?

The derivative of axcos(3x+bxsin(3x)) is a(cos(3x)-3xsin(3x))+b(sin(3x)+3xcos(3x))

What is the first derivative of axcos(3x+bxsin(3x)) ?

The first derivative of axcos(3x+bxsin(3x)) is a(cos(3x)-3xsin(3x))+b(sin(3x)+3xcos(3x))

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\frac{d}{d x} (a x cos (3 x) + b x sin (3 x))

a (cos (3 x) - 3 x sin (3 x)) + b (sin (3 x) + 3 x cos (3 x))

Solution steps

\frac{d}{d x} (a x cos (3 x) + b x sin (3 x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (a x cos (3 x)) + \frac{d}{d x} (b x sin (3 x))

\frac{d}{d x} (a x cos (3 x)) = a (cos (3 x) - 3 x sin (3 x))

\frac{d}{d x} (b x sin (3 x)) = b (sin (3 x) + 3 x cos (3 x))

= a (cos (3 x) - 3 x sin (3 x)) + b (sin (3 x) + 3 x cos (3 x))

\int \frac{2}{t ^{2}} d t

\int (x^{3} - sin (x)) d x

\int \frac{1}{cos ^{2} ( 5 x )} d x

x \to 1 lim (\frac{2 \cdot x + 3}{x + 4})

\int \frac{x + 1}{3 - 2 x - x ^{2}} d x

What is the derivative of axcos(3x+bxsin(3x)) ?
The derivative of axcos(3x+bxsin(3x)) is a(cos(3x)-3xsin(3x))+b(sin(3x)+3xcos(3x))
What is the first derivative of axcos(3x+bxsin(3x)) ?
The first derivative of axcos(3x+bxsin(3x)) is a(cos(3x)-3xsin(3x))+b(sin(3x)+3xcos(3x))