What is the derivative of f(x)=-cot(x)csc(x) ?

The derivative of f(x)=-cot(x)csc(x) is -csc(x)+2csc^3(x)

What is the first derivative of f(x)=-cot(x)csc(x) ?

The first derivative of f(x)=-cot(x)csc(x) is -csc(x)+2csc^3(x)

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derivative of

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

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

Solution steps

\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)

f (x) = x (ln (x)) - x

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

\int \frac{( 7 x ^{2} + x + 7 )}{( x ^{2} + 1 ) ^{2}} d x

\int \frac{x ^{3} + 1}{x ^{2} - 4} d x

What is the derivative of f(x)=-cot(x)csc(x) ?
The derivative of f(x)=-cot(x)csc(x) is -csc(x)+2csc^3(x)
What is the first derivative of f(x)=-cot(x)csc(x) ?
The first derivative of f(x)=-cot(x)csc(x) is -csc(x)+2csc^3(x)