What is the derivative of asin(bx+c+d) ?

The derivative of asin(bx+c+d) is abcos(bx+c)

What is the first derivative of asin(bx+c+d) ?

The first derivative of asin(bx+c+d) is abcos(bx+c)

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

ab cos (b x + c)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{dd}{d x} = 0

= a cos (b x + c) b + 0

Simplify

= ab cos (b x + c)

What is the derivative of asin(bx+c+d) ?
The derivative of asin(bx+c+d) is abcos(bx+c)
What is the first derivative of asin(bx+c+d) ?
The first derivative of asin(bx+c+d) is abcos(bx+c)