What is the derivative of acos(3x+bsin(3x)) ?

The derivative of acos(3x+bsin(3x)) is -3asin(3x)+bcos(3x)*3

What is the first derivative of acos(3x+bsin(3x)) ?

The first derivative of acos(3x+bsin(3x)) is -3asin(3x)+bcos(3x)*3

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

\int (3 t^{2} - 4 t - 4) d t

sin^{3} (x^{3} - 2 x)

\int_{0}^{3} t e^{- t} d t

\int 6 x^{2} - 5 x + 3 d x

\int (6 sin (2 x) - 4 cos (4 x)) d x

What is the derivative of acos(3x+bsin(3x)) ?
The derivative of acos(3x+bsin(3x)) is -3asin(3x)+bcos(3x)*3
What is the first derivative of acos(3x+bsin(3x)) ?
The first derivative of acos(3x+bsin(3x)) is -3asin(3x)+bcos(3x)*3