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

The derivative of (sqrt(x)/(sin(x))) is (csc(x))/(2sqrt(x))-sqrt(x)cot(x)csc(x)

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

The first derivative of (sqrt(x)/(sin(x))) is (csc(x))/(2sqrt(x))-sqrt(x)cot(x)csc(x)

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

\frac{csc ( x )}{2 x} - x cot (x) csc (x)

Solution steps

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

Simplify

\frac{x}{sin ( x )} : x csc (x)

= \frac{d}{d x} (x csc (x))

Apply the Product Rule:

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

f = x, g = csc (x)

= \frac{d}{d x} (x) csc (x) + \frac{d}{d x} (csc (x)) x

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

= \frac{1}{2 x} csc (x) + (- cot (x) csc (x)) x

Simplify

\frac{1}{2 x} csc (x) + (- cot (x) csc (x)) x : \frac{csc ( x )}{2 x} - x cot (x) csc (x)

= \frac{csc ( x )}{2 x} - x cot (x) csc (x)

\frac{\partial ^{2}}{\partial y ^{2}} (sin^{2} (m x + n y))

\int \frac{x ^{2}}{4 x ^{2} + 9} d x

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

3 x^{2}, x^{3}

\frac{\partial}{\partial x} (e^{7 x + 3 y})

What is the derivative of (sqrt(x)/(sin(x))) ?
The derivative of (sqrt(x)/(sin(x))) is (csc(x))/(2sqrt(x))-sqrt(x)cot(x)csc(x)
What is the first derivative of (sqrt(x)/(sin(x))) ?
The first derivative of (sqrt(x)/(sin(x))) is (csc(x))/(2sqrt(x))-sqrt(x)cot(x)csc(x)