What is the derivative of f(x)=6x^2cot(x) ?

The derivative of f(x)=6x^2cot(x) is 6(2xcot(x)-x^2csc^2(x))

What is the first derivative of f(x)=6x^2cot(x) ?

The first derivative of f(x)=6x^2cot(x) is 6(2xcot(x)-x^2csc^2(x))

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derivative of

f (x) = 6 x^{2} cot (x)

6 (2 x cot (x) - x^{2} csc^{2} (x))

Solution steps

\frac{d}{d x} (6 x^{2} cot (x))

Take the constant out:

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

= 6 \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)

= 6 (\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)

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

Simplify

= 6 (2 x cot (x) - x^{2} csc^{2} (x))

x \to \infty lim (2 x - 2 x)

\frac{d}{d x} (x^{8} cos (x))

\frac{\partial}{\partial y} (y^{4} + 5 x y^{3})

\int (54) d x

\int \frac{9 x ^{2}}{1 - x ^{3}} d x

What is the derivative of f(x)=6x^2cot(x) ?
The derivative of f(x)=6x^2cot(x) is 6(2xcot(x)-x^2csc^2(x))
What is the first derivative of f(x)=6x^2cot(x) ?
The first derivative of f(x)=6x^2cot(x) is 6(2xcot(x)-x^2csc^2(x))