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

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

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

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

cos (2 x)

Solution steps

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

Apply the Product Rule:

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

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

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

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

Simplify

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

= cos (2 x)

x \to + (- 1) lim (x + 2 x^{4})

- \frac{1}{( x - 5 ) ^{2}}

\frac{d}{d x} (e^{x^{0}})

\int_{1}^{3} \frac{x}{( 2 x - 1 ) ^{3}} d x

\int x ln (5 x) d x

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