What is the derivative of (xsin(2x)^{3/2}) ?

The derivative of (xsin(2x)^{3/2}) is (3(sin(2x)+2xcos(2x))(xsin(2x))^{1/2})/2

What is the first derivative of (xsin(2x)^{3/2}) ?

The first derivative of (xsin(2x)^{3/2}) is (3(sin(2x)+2xcos(2x))(xsin(2x))^{1/2})/2

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

\frac{3 ( sin ( 2 x ) + 2 x cos ( 2 x ) ) ( x sin ( 2 x ) ) ^{\frac{1}{2}}}{2}

Solution steps

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

Apply the chain rule:

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

= \frac{3 ( x sin ( 2 x ) ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (x sin (2 x))

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

= \frac{3 ( x sin ( 2 x ) ) ^{\frac{1}{2}}}{2} (sin (2 x) + 2 x cos (2 x))

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 ( sin ( 2 x ) + 2 x cos ( 2 x ) ) ( x sin ( 2 x ) ) ^{\frac{1}{2}}}{2}

\int \frac{( x + 16 )}{( x ^{2} + 2 x - 8 )} d x

\frac{\partial}{\partial α} (K (α) (α)^{α} L^{1 - α})

y = 11 x^{2}, (- 2, 44)

\int \frac{1}{r ( 2 - r ^{2} )} d r

x \to 1 lim (\frac{3 x}{x ^{2} - 1})

What is the derivative of (xsin(2x)^{3/2}) ?
The derivative of (xsin(2x)^{3/2}) is (3(sin(2x)+2xcos(2x))(xsin(2x))^{1/2})/2
What is the first derivative of (xsin(2x)^{3/2}) ?
The first derivative of (xsin(2x)^{3/2}) is (3(sin(2x)+2xcos(2x))(xsin(2x))^{1/2})/2