What is the derivative of 11x^4cot(x) ?

The derivative of 11x^4cot(x) is 11(4x^3cot(x)-x^4csc^2(x))

What is the first derivative of 11x^4cot(x) ?

The first derivative of 11x^4cot(x) is 11(4x^3cot(x)-x^4csc^2(x))

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\frac{d}{d x} (11 x^{4} cot (x))

11 (4 x^{3} cot (x) - x^{4} csc^{2} (x))

Solution steps

\frac{d}{d x} (11 x^{4} cot (x))

Take the constant out:

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

= 11 \frac{d}{d x} (x^{4} cot (x))

Apply the Product Rule:

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

f = x^{4}, g = cot (x)

= 11 (\frac{d}{d x} (x^{4}) cot (x) + \frac{d}{d x} (cot (x)) x^{4})

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= 11 (4 x^{3} cot (x) + (- csc^{2} (x)) x^{4})

Simplify

= 11 (4 x^{3} cot (x) - x^{4} csc^{2} (x))

x^{3} + 1, 0, - 2, 1

\int - 3 x \cdot sin (x) d x

x \to 3 lim (2 x - 4)

\int_{0}^{4} 3 x - \frac{3 x}{2} d x

\int x sec (x^{2}) d x

What is the derivative of 11x^4cot(x) ?
The derivative of 11x^4cot(x) is 11(4x^3cot(x)-x^4csc^2(x))
What is the first derivative of 11x^4cot(x) ?
The first derivative of 11x^4cot(x) is 11(4x^3cot(x)-x^4csc^2(x))