What is the derivative of 8x^3cot(x) ?

The derivative of 8x^3cot(x) is 8(3x^2cot(x)-x^3csc^2(x))

What is the first derivative of 8x^3cot(x) ?

The first derivative of 8x^3cot(x) is 8(3x^2cot(x)-x^3csc^2(x))

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derivative of

8 x^{3} cot (x)

8 (3 x^{2} cot (x) - x^{3} csc^{2} (x))

Solution steps

\frac{d}{d x} (8 x^{3} cot (x))

Take the constant out:

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

= 8 \frac{d}{d x} (x^{3} cot (x))

Apply the Product Rule:

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

f = x^{3}, g = cot (x)

= 8 (\frac{d}{d x} (x^{3}) cot (x) + \frac{d}{d x} (cot (x)) x^{3})

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= 8 (3 x^{2} cot (x) + (- csc^{2} (x)) x^{3})

Simplify

= 8 (3 x^{2} cot (x) - x^{3} csc^{2} (x))

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

\int \frac{x ^{7}}{x ^{4} - 2} d x

\int 2 x cos (y) d x

\int \frac{t}{1 + t ^{2}} d t

\int_{0}^{\frac{1}{8}} x arcsin (8 x) d x

What is the derivative of 8x^3cot(x) ?
The derivative of 8x^3cot(x) is 8(3x^2cot(x)-x^3csc^2(x))
What is the first derivative of 8x^3cot(x) ?
The first derivative of 8x^3cot(x) is 8(3x^2cot(x)-x^3csc^2(x))