What is the derivative of y=2xsin(x) ?

The derivative of y=2xsin(x) is 2(sin(x)+xcos(x))

What is the first derivative of y=2xsin(x) ?

The first derivative of y=2xsin(x) is 2(sin(x)+xcos(x))

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derivative of

y = 2 x sin (x)

2 (sin (x) + x cos (x))

Solution steps

\frac{d}{d x} (2 x sin (x))

Take the constant out:

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

= 2 \frac{d}{d x} (x sin (x))

Apply the Product Rule:

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

f = x, g = sin (x)

= 2 (\frac{d x}{d x} sin (x) + \frac{d}{d x} (sin (x)) x)

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

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

= 2 (1 \cdot sin (x) + cos (x) x)

Simplify

= 2 (sin (x) + x cos (x))

x \to 0 lim (\frac{4 x}{∣ x ∣})

y^{^{''}} - 8 y^{^{'}} = 5 t

y^{^{''}} + 4 y^{^{'}} + 4 y = 12 t + 16, y (0) = 3, y^{^{'}} (0) = - 4

\frac{d}{d x} (\frac{2 ^{0}}{3 ^{1} + 0})

n \to \infty lim (n)

What is the derivative of y=2xsin(x) ?
The derivative of y=2xsin(x) is 2(sin(x)+xcos(x))
What is the first derivative of y=2xsin(x) ?
The first derivative of y=2xsin(x) is 2(sin(x)+xcos(x))