What is (\partial)/(\partial x)(x/(10)cos(5x)) ?

The answer to (\partial)/(\partial x)(x/(10)cos(5x)) is 1/10 (cos(5x)-5xsin(5x))

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(\partial)/(\partial x)(x/(10)cos(5x))

\frac{\partial}{\partial x} (\frac{x}{10} cos (5 x))

\frac{1}{10} (cos (5 x) - 5 x sin (5 x))

Solution steps

\frac{\partial}{\partial x} (\frac{x}{10} cos (5 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{10} \frac{\partial}{\partial x} (x cos (5 x))

Apply the Product Rule:

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

f = x, g = cos (5 x)

= \frac{1}{10} (\frac{\partial}{\partial x} (x) cos (5 x) + \frac{\partial}{\partial x} (cos (5 x)) x)

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (cos (5 x)) = - sin (5 x) \cdot 5

= \frac{1}{10} (1 \cdot cos (5 x) + (- sin (5 x) \cdot 5) x)

Simplify

= \frac{1}{10} (cos (5 x) - 5 x sin (5 x))

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What is (\partial)/(\partial x)(x/(10)cos(5x)) ?
The answer to (\partial)/(\partial x)(x/(10)cos(5x)) is 1/10 (cos(5x)-5xsin(5x))