What is the derivative of (-cos(x))/(sin^2(x)) ?

The derivative of (-cos(x))/(sin^2(x)) is -csc(x)+2csc^3(x)

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

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

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derivative of

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

- csc (x) + 2 csc^{3} (x)

Solution steps

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

Simplify

\frac{- cos ( x )}{sin ^{2} ( x )} : - cot (x) csc (x)

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = cot (x), g = csc (x)

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

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

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

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

Simplify

- ((- csc^{2} (x)) csc (x) + (- cot (x) csc (x)) cot (x)) : - csc (x) + 2 csc^{3} (x)

= - csc (x) + 2 csc^{3} (x)

d er i v a t i v e (lo g_{10} (x^{3} + 4))^{5}

d er i v a t i v e e^{c o s^{2} (x)}

d er i v a t i v e - 2 sin^{2} (x)

d er i v a t i v e \frac{1}{( x ^{2} + x )}

d er i v a t i v e (x + 3)^{\frac{1}{2}}

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