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

The derivative of 2xsqrt(x)sin(x) is 3sqrt(x)sin(x)+2x^{3/2}cos(x)

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

The first derivative of 2xsqrt(x)sin(x) is 3sqrt(x)sin(x)+2x^{3/2}cos(x)

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

3 x sin (x) + 2 x^{\frac{3}{2}} cos (x)

Solution steps

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

Simplify

2 x x sin (x) : 2 x^{\frac{3}{2}} sin (x)

= \frac{d}{d x} (2 x^{\frac{3}{2}} sin (x))

Take the constant out:

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

= 2 \frac{d}{d x} (x^{\frac{3}{2}} sin (x))

Apply the Product Rule:

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

f = x^{\frac{3}{2}}, g = sin (x)

= 2 (\frac{d}{d x} (x^{\frac{3}{2}}) sin (x) + \frac{d}{d x} (sin (x)) x^{\frac{3}{2}})

\frac{d}{d x} (x^{\frac{3}{2}}) = \frac{3 x}{2}

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

= 2 (\frac{3 x}{2} sin (x) + cos (x) x^{\frac{3}{2}})

Simplify

2 (\frac{3 x}{2} sin (x) + cos (x) x^{\frac{3}{2}}) : 3 x sin (x) + 2 x^{\frac{3}{2}} cos (x)

= 3 x sin (x) + 2 x^{\frac{3}{2}} cos (x)

\int (2 cos (x))^{2} d x

\frac{\partial}{\partial y} (5)

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

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

y^{^{''}} + 4 y^{^{'}} = 17 cos (t), y (0) = - 1, y^{^{'}} (0) = 0

What is the derivative of 2xsqrt(x)sin(x) ?
The derivative of 2xsqrt(x)sin(x) is 3sqrt(x)sin(x)+2x^{3/2}cos(x)
What is the first derivative of 2xsqrt(x)sin(x) ?
The first derivative of 2xsqrt(x)sin(x) is 3sqrt(x)sin(x)+2x^{3/2}cos(x)