What is the derivative of f(x)=8x^2cot(x) ?

The derivative of f(x)=8x^2cot(x) is 8(2xcot(x)-x^2csc^2(x))

What is the first derivative of f(x)=8x^2cot(x) ?

The first derivative of f(x)=8x^2cot(x) is 8(2xcot(x)-x^2csc^2(x))

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derivative of

f (x) = 8 x^{2} cot (x)

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

Solution steps

\frac{d}{d x} (8 x^{2} cot (x))

Take the constant out:

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

= 8 \frac{d}{d x} (x^{2} cot (x))

Apply the Product Rule:

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

f = x^{2}, g = cot (x)

= 8 (\frac{d}{d x} (x^{2}) cot (x) + \frac{d}{d x} (cot (x)) x^{2})

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

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

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

Simplify

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

\frac{d}{d t} (\frac{t}{1 + t})

n = 1 \sum \infty \frac{1}{n e ^{n}}

\frac{d ^{6}}{d x ^{6}} (x^{- 6})

\frac{\partial}{\partial x} ((x^{2} - a - 1) (x^{2} + a - 1))

\frac{\partial}{\partial x} (3 x^{2} + y^{2})

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