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Popular >

derivative of x^3cot(x)

Solution

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

Solution

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

Solution steps

\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)

= \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)

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

Simplify

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

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Frequently Asked Questions (FAQ)

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