What is the derivative of-9cot(xcsc(x)) ?

The derivative of-9cot(xcsc(x)) is -9(csc(x)-2csc^3(x))

What is the first derivative of-9cot(xcsc(x)) ?

The first derivative of-9cot(xcsc(x)) is -9(csc(x)-2csc^3(x))

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\frac{d}{d x} (- 9 cot (x) csc (x))

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

Solution steps

\frac{d}{d x} (- 9 cot (x) csc (x))

Take the constant out:

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

= - 9 \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)

= - 9 (\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)

= - 9 ((- csc^{2} (x)) csc (x) + (- cot (x) csc (x)) cot (x))

Simplify

- 9 ((- csc^{2} (x)) csc (x) + (- cot (x) csc (x)) cot (x)) : - 9 (csc (x) - 2 csc^{3} (x))

= - 9 (csc (x) - 2 csc^{3} (x))

\frac{d}{d x} (ln (\frac{3 + e ^{x}}{3 - e ^{x}}))

\frac{d}{d x} (a x^{4} + b x^{3} + c x^{2})

(3 x - 1)^{7} (2 x + 1)^{5}

\frac{d}{d y} (e^{2 y})

f (x) = x^{6} (x - 1)^{5}

What is the derivative of-9cot(xcsc(x)) ?
The derivative of-9cot(xcsc(x)) is -9(csc(x)-2csc^3(x))
What is the first derivative of-9cot(xcsc(x)) ?
The first derivative of-9cot(xcsc(x)) is -9(csc(x)-2csc^3(x))