What is the derivative of 2x*sin(x) ?

The derivative of 2x*sin(x) is 2(sin(x)+xcos(x))

What is the first derivative of 2x*sin(x) ?

The first derivative of 2x*sin(x) is 2(sin(x)+xcos(x))

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

\frac{d}{d x} (sin^{2} (\frac{5 π}{6}))

\frac{d}{d x} (2 tan (x) - tan^{2} (x))

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

\frac{9 s}{9 s ^{2} + 1}

\int \frac{( x + 6 )}{( x + 2 ) ^{2}} d x

What is the derivative of 2x*sin(x) ?
The derivative of 2x*sin(x) is 2(sin(x)+xcos(x))
What is the first derivative of 2x*sin(x) ?
The first derivative of 2x*sin(x) is 2(sin(x)+xcos(x))