What is the derivative of asin(x+bcos(x)) ?

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

What is the first derivative of asin(x+bcos(x)) ?

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

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

a cos (x) - b sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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