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

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

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

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

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derivative of

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

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

Solution steps

\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)

= \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)

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

Simplify

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

\int cos (ln (x)) d x

\int \frac{x ^{2}}{49 + x ^{2}} d x

\int x (1 + x^{3}) d x

y^{^{'}} + y = 2, y (0) = 0

(- 5.3) (7.9)

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