What is the derivative of-3cot(x)csc(x) ?

The derivative of-3cot(x)csc(x) is -3csc(x)+6csc^3(x)

What is the first derivative of-3cot(x)csc(x) ?

The first derivative of-3cot(x)csc(x) is -3csc(x)+6csc^3(x)

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derivative of

- 3 cot (x) csc (x)

- 3 csc (x) + 6 csc^{3} (x)

Solution steps

\frac{d}{d x} (- 3 cot (x) csc (x))

Take the constant out:

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

= - 3 \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)

= - 3 (\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)

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

Simplify

- 3 ((- csc^{2} (x)) csc (x) + (- cot (x) csc (x)) cot (x)) : - 3 csc (x) + 6 csc^{3} (x)

= - 3 csc (x) + 6 csc^{3} (x)

\int e^{x^{2}} \cdot x ln (x) d x

y^{^{'}} + \frac{3 y}{100 - x} = \frac{4}{5}

\int \frac{tan ^{3} ( ln ( x ) )}{4 x} d x

\int t cos^{2} (t) d t

ln (2)

What is the derivative of-3cot(x)csc(x) ?
The derivative of-3cot(x)csc(x) is -3csc(x)+6csc^3(x)
What is the first derivative of-3cot(x)csc(x) ?
The first derivative of-3cot(x)csc(x) is -3csc(x)+6csc^3(x)