What is (\partial)/(\partial x)(cos(x)*sin(x)) ?

The answer to (\partial)/(\partial x)(cos(x)*sin(x)) is cos(2x)

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(\partial)/(\partial x)(cos(x)*sin(x))

\frac{\partial}{\partial x} (cos (x) \cdot sin (x))

cos (2 x)

Solution steps

\frac{\partial}{\partial x} (cos (x) sin (x))

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(- sin (x)) sin (x) + cos (x) cos (x) : cos (2 x)

= cos (2 x)

\frac{d}{d x} (1 + e^{x^{2}})

\frac{d}{d x} (ln ∣ ln (x) ∣)

y = x^{(\frac{1}{l n ( x )})}

\int sin^{5} (x) \cdot cos^{5} (x) d x

x \to 0 lim (\frac{7}{cos ( x )})

What is (\partial)/(\partial x)(cos(x)*sin(x)) ?
The answer to (\partial)/(\partial x)(cos(x)*sin(x)) is cos(2x)