What is the derivative of x^{-1/2}sin(x) ?

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

What is the first derivative of x^{-1/2}sin(x) ?

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x^{- \frac{1}{2}}, g = sin (x)

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

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

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

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

Simplify

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

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

n = 1 \sum \infty \frac{6}{n ^{2} + 2 n}

\int_{1}^{10} \frac{21}{x ^{3}} d x

x \to - 1 lim (\frac{4}{( x + 1 ) ^{2}})

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

x \to 4 - lim (\frac{1}{4 - x})

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