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) 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{1}{2}, 7), (3, - \frac{3}{2})

f (t) = \frac{( t ^{2} - 4 t )}{t + 3}

\int \frac{2 x + 3}{x ^{2} + 3 x + 4} d x

x \to 0 + lim (x^{n})

\frac{\partial}{\partial x} (8 x e^{x^{2}} + y^{2})

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