What is the derivative of (x^2)/(tan(x)) ?

The derivative of (x^2)/(tan(x)) is 2xcot(x)-x^2csc^2(x)

What is the first derivative of (x^2)/(tan(x)) ?

The first derivative of (x^2)/(tan(x)) is 2xcot(x)-x^2csc^2(x)

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derivative of

\frac{x ^{2}}{tan ( x )}

2 x cot (x) - x^{2} csc^{2} (x)

Solution steps

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

Simplify

\frac{x ^{2}}{tan ( x )} : x^{2} cot (x)

= \frac{d}{d x} (x^{2} cot (x))

Apply the Product Rule:

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

f = x^{2}, g = cot (x)

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

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

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

= 2 x cot (x) + (- csc^{2} (x)) x^{2}

Simplify

= 2 x cot (x) - x^{2} csc^{2} (x)

y = 4 cos (4 x^{2})

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

\frac{1}{( 2 x + 1 )}

\frac{ln ( 1 )}{x}

(6 x^{2} + 11)^{\frac{1}{2}}

What is the derivative of (x^2)/(tan(x)) ?
The derivative of (x^2)/(tan(x)) is 2xcot(x)-x^2csc^2(x)
What is the first derivative of (x^2)/(tan(x)) ?
The first derivative of (x^2)/(tan(x)) is 2xcot(x)-x^2csc^2(x)