What is the derivative of a(1-cos(x)) ?

The derivative of a(1-cos(x)) is asin(x)

What is the first derivative of a(1-cos(x)) ?

The first derivative of a(1-cos(x)) is asin(x)

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\frac{d}{d x} (a (1 - cos (x)))

a sin (x)

Solution steps

\frac{d}{d x} (a (1 - cos (x)))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= a \frac{d}{d x} (1 - cos (x))

Apply the Sum/Difference Rule:

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

= a (\frac{d}{d x} (1) - \frac{d}{d x} (cos (x)))

\frac{d}{d x} (1) = 0

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

= a (0 - (- sin (x)))

Simplify

= a sin (x)

What is the derivative of a(1-cos(x)) ?
The derivative of a(1-cos(x)) is asin(x)
What is the first derivative of a(1-cos(x)) ?
The first derivative of a(1-cos(x)) is asin(x)