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

The derivative of sin(x(1-cos(x))) is cos(x)(1-cos(x))+sin^2(x)

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

The first derivative of sin(x(1-cos(x))) is cos(x)(1-cos(x))+sin^2(x)

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

cos (x) (1 - cos (x)) + sin^{2} (x)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (x), g = 1 - cos (x)

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

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

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

= cos (x) (1 - cos (x)) + sin (x) sin (x)

sin (x) sin (x) = sin^{2} (x)

= cos (x) (1 - cos (x)) + sin^{2} (x)

What is the derivative of sin(x(1-cos(x))) ?
The derivative of sin(x(1-cos(x))) is cos(x)(1-cos(x))+sin^2(x)
What is the first derivative of sin(x(1-cos(x))) ?
The first derivative of sin(x(1-cos(x))) is cos(x)(1-cos(x))+sin^2(x)