What is the derivative of xcos(4x) ?

The derivative of xcos(4x) is cos(4x)-4xsin(4x)

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

The first derivative of xcos(4x) is cos(4x)-4xsin(4x)

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

cos (4 x) - 4 x sin (4 x)

Solution steps

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

Apply the Product Rule:

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

f = x, g = cos (4 x)

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

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

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

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

Simplify

= cos (4 x) - 4 x sin (4 x)

\int \frac{t ^{4} + 1}{t ^{5} + 4 t ^{3}} d t

(x^{2} + 1) y^{^{'}} + 9 x (y - 1) = 0, y (0) = 4

\int u^{2} u^{3} + 2 d u

sin (x^{7})

y + 2 t^{2} + y^{^{'}} t ln (t) = 0

What is the derivative of xcos(4x) ?
The derivative of xcos(4x) is cos(4x)-4xsin(4x)
What is the first derivative of xcos(4x) ?
The first derivative of xcos(4x) is cos(4x)-4xsin(4x)