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Popular >

derivative of x/(sin(x))

Solution

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

Solution

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

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

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

= 1 \cdot csc (x) + (- cot (x) csc (x)) x

Simplify

= csc (x) - x cot (x) csc (x)

Popular Examples

(\partial)/(\partial x)(x^{1/4})

\frac{\partial}{\partial x} (x^{\frac{1}{4}})

limit as x approaches 1 of 2x+3

x \to 1 lim (2 x + 3)

integral of cos(2x)cos(6x)

\int cos (2 x) cos (6 x) d x

integral from-r to r of 4(r^2-x^2)

\int_{- r}^{r} 4 (r^{2} - x^{2}) d x

derivative of (4x)^{8x}derivative of

(4 x)^{8 x}

Frequently Asked Questions (FAQ)

What is the derivative of x/(sin(x)) ?
The derivative of x/(sin(x)) is csc(x)-xcot(x)csc(x)
What is the first derivative of x/(sin(x)) ?
The first derivative of x/(sin(x)) is csc(x)-xcot(x)csc(x)