What is the derivative of f(x)=6x^3cot(x) ?

The derivative of f(x)=6x^3cot(x) is 6(3x^2cot(x)-x^3csc^2(x))

What is the first derivative of f(x)=6x^3cot(x) ?

The first derivative of f(x)=6x^3cot(x) is 6(3x^2cot(x)-x^3csc^2(x))

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derivative of

f (x) = 6 x^{3} cot (x)

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

Solution steps

\frac{d}{d x} (6 x^{3} cot (x))

Take the constant out:

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

= 6 \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)

= 6 (\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)

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

Simplify

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

What is the derivative of f(x)=6x^3cot(x) ?
The derivative of f(x)=6x^3cot(x) is 6(3x^2cot(x)-x^3csc^2(x))
What is the first derivative of f(x)=6x^3cot(x) ?
The first derivative of f(x)=6x^3cot(x) is 6(3x^2cot(x)-x^3csc^2(x))