What is the derivative of a(x-sin(x)) ?

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

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

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

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\frac{d}{d x} (a (x - sin (x)))

a (1 - cos (x))

Solution steps

\frac{d}{d x} (a (x - sin (x)))

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{d x}{d x} = 1

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

= a (1 - cos (x))

t an g e n t y = 4 x - x^{2} (1.3)

y^{^{'}} = x^{2} + x, y (1) = 3

\int sin^{3} (6 x) cos^{2} (6 x) d x

\int_{0}^{3} π (\frac{1}{x + 5})^{2} d x

a re a y = 3 x + 1, y = x + 1

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