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)

Simplify

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

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

\frac{d}{d x} (sin (3 x + 4 y))

\frac{d}{d x} (x^{3} + 2 x^{2} + x)

cos^{2} (z)

\int 7 x^{5} e^{- x^{3}} d x

\int x (y) d 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)