What is the derivative of xcos(5x) ?

The derivative of xcos(5x) is cos(5x)-5xsin(5x)

What is the first derivative of xcos(5x) ?

The first derivative of xcos(5x) is cos(5x)-5xsin(5x)

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\frac{d}{d x} (x cos (5 x))

cos (5 x) - 5 x sin (5 x)

Solution steps

\frac{d}{d 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{d x}{d x} cos (5 x) + \frac{d}{d x} (cos (5 x)) x

\frac{d x}{d x} = 1

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

= 1 \cdot cos (5 x) + (- sin (5 x) \cdot 5) x

Simplify

= cos (5 x) - 5 x sin (5 x)

x \to 1 lim (9 - 4 x^{2})

x = 6 y^{2}, x = 4 + 5 y^{2}

x \to - 6 + lim (x^{2} + 6)

x y^{^{'}} - 2 y = - 2 x^{2} - x + 1

\frac{d}{d x} ((2 x + 7)^{2})

What is the derivative of xcos(5x) ?
The derivative of xcos(5x) is cos(5x)-5xsin(5x)
What is the first derivative of xcos(5x) ?
The first derivative of xcos(5x) is cos(5x)-5xsin(5x)