What is the derivative of sin(x+x*cos(x)) ?

The derivative of sin(x+x*cos(x)) is 2cos(x)-xsin(x)

What is the first derivative of sin(x+x*cos(x)) ?

The first derivative of sin(x+x*cos(x)) is 2cos(x)-xsin(x)

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\frac{d}{d x} (sin (x) + x \cdot cos (x))

2 cos (x) - x sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= 2 cos (x) - x sin (x)

\frac{d}{d x} (x^{2} y - x)

\int (cos (5 x) cos (3 x)) d x

\int_{0}^{1} x - x^{3} d x

\frac{\partial}{\partial x} (e^{- x^{3} - y^{3}})

5^{t}

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