What is the derivative of (sin(0.5sqrt(x))/x) ?

The derivative of (sin(0.5sqrt(x))/x) is (0.25sqrt(x)cos(0.5sqrt(x))-sin(0.5sqrt(x)))/(x^2)

What is the first derivative of (sin(0.5sqrt(x))/x) ?

The first derivative of (sin(0.5sqrt(x))/x) is (0.25sqrt(x)cos(0.5sqrt(x))-sin(0.5sqrt(x)))/(x^2)

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\frac{d}{d x} (\frac{sin ( 0.5 x )}{x})

\frac{0.25 x cos ( 0.5 x ) - sin ( 0.5 x )}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{sin ( 0.5 x )}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( sin ( 0.5 x ) ) x - \frac{d x}{d x} sin ( 0.5 x )}{x ^{2}}

\frac{d}{d x} (sin (0.5 x)) = \frac{0.25 cos ( 0.5 x )}{x}

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

= \frac{\frac{0.25 c o s ( 0.5 x )}{x} x - 1 \cdot sin ( 0.5 x )}{x ^{2}}

Simplify

\frac{\frac{0.25 c o s ( 0.5 x )}{x} x - 1 \cdot sin ( 0.5 x )}{x ^{2}} : \frac{0.25 x cos ( 0.5 x ) - sin ( 0.5 x )}{x ^{2}}

= \frac{0.25 x cos ( 0.5 x ) - sin ( 0.5 x )}{x ^{2}}

\int - \frac{2000 x}{( 1 + x ^{2} )} d x

t an g e n t x^{2}, at x = 2

\frac{\partial}{\partial x} (3 x y^{2} + 20 x^{2} y^{3})

y^{^{''}} + 2 y^{^{'}} + 2 y = 0, y (\frac{π}{4}) = 2, y^{^{'}} (\frac{π}{4}) = - 2

\int \frac{3 x ^{2} + 17 x + 32}{x ^{3} + 8 x ^{2} + 16 x} d x

What is the derivative of (sin(0.5sqrt(x))/x) ?
The derivative of (sin(0.5sqrt(x))/x) is (0.25sqrt(x)cos(0.5sqrt(x))-sin(0.5sqrt(x)))/(x^2)
What is the first derivative of (sin(0.5sqrt(x))/x) ?
The first derivative of (sin(0.5sqrt(x))/x) is (0.25sqrt(x)cos(0.5sqrt(x))-sin(0.5sqrt(x)))/(x^2)