What is the derivative of xsin(4x) ?

The derivative of xsin(4x) is sin(4x)+4xcos(4x)

What is the first derivative of xsin(4x) ?

The first derivative of xsin(4x) is sin(4x)+4xcos(4x)

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\frac{d}{d x} (x sin (4 x))

sin (4 x) + 4 x cos (4 x)

Solution steps

\frac{d}{d x} (x sin (4 x))

Apply the Product Rule:

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

f = x, g = sin (4 x)

= \frac{d x}{d x} sin (4 x) + \frac{d}{d x} (sin (4 x)) x

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

\frac{d}{d x} (sin (4 x)) = cos (4 x) \cdot 4

= 1 \cdot sin (4 x) + cos (4 x) \cdot 4 x

Simplify

= sin (4 x) + 4 x cos (4 x)

f (x) = cos (\frac{π x}{2}), at x = 0.4

\int 30 e^{- x} d x

\frac{\partial}{\partial x} (9 x y)

x \to - 1 + lim (ln (x + 1))

\frac{d}{d x} ((x - 4) (x + 1) (x + 5))

What is the derivative of xsin(4x) ?
The derivative of xsin(4x) is sin(4x)+4xcos(4x)
What is the first derivative of xsin(4x) ?
The first derivative of xsin(4x) is sin(4x)+4xcos(4x)