What is the derivative of (xsin(4x)/8) ?

The derivative of (xsin(4x)/8) is 1/8 (sin(4x)+4xcos(4x))

What is the first derivative of (xsin(4x)/8) ?

The first derivative of (xsin(4x)/8) is 1/8 (sin(4x)+4xcos(4x))

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\frac{d}{d x} (\frac{x sin ( 4 x )}{8})

\frac{1}{8} (sin (4 x) + 4 x cos (4 x))

Solution steps

\frac{d}{d x} (\frac{x sin ( 4 x )}{8})

Take the constant out:

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

= \frac{1}{8} \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{1}{8} (\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

= \frac{1}{8} (1 \cdot sin (4 x) + cos (4 x) \cdot 4 x)

Simplify

= \frac{1}{8} (sin (4 x) + 4 x cos (4 x))

6 y^{^{''}} + 4 y^{^{'}} + 7 y = 0

f (x) = 2 x^{2} + x - 1

y^{^{''}} + 9 y = 0, y (\frac{π}{2}) = 1, y^{^{'}} (\frac{π}{2}) = - 3

\frac{d y}{d x}, 9 y + x = 4 y

\int (6 x^{2} - 4 e^{x}) d x

What is the derivative of (xsin(4x)/8) ?
The derivative of (xsin(4x)/8) is 1/8 (sin(4x)+4xcos(4x))
What is the first derivative of (xsin(4x)/8) ?
The first derivative of (xsin(4x)/8) is 1/8 (sin(4x)+4xcos(4x))