What is the derivative of xsin(6x) ?

The derivative of xsin(6x) is sin(6x)+6xcos(6x)

What is the first derivative of xsin(6x) ?

The first derivative of xsin(6x) is sin(6x)+6xcos(6x)

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\frac{d}{d x} (x sin (6 x))

sin (6 x) + 6 x cos (6 x)

Solution steps

\frac{d}{d x} (x sin (6 x))

Apply the Product Rule:

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

f = x, g = sin (6 x)

= \frac{d x}{d x} sin (6 x) + \frac{d}{d x} (sin (6 x)) x

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

\frac{d}{d x} (sin (6 x)) = cos (6 x) \cdot 6

= 1 \cdot sin (6 x) + cos (6 x) \cdot 6 x

Simplify

= sin (6 x) + 6 x cos (6 x)

\int 16 y^{3} + 9 y^{2} - 6 y + 3 d y

\int_{0}^{1} 4^{4 x} d x

\int \frac{cos ( x )}{sin ^{2} ( x ) - 64} d x

\int cos (2 π) d x

What is the derivative of xsin(6x) ?
The derivative of xsin(6x) is sin(6x)+6xcos(6x)
What is the first derivative of xsin(6x) ?
The first derivative of xsin(6x) is sin(6x)+6xcos(6x)