What is the derivative of 2x^2cos(xcot(x)) ?

The derivative of 2x^2cos(xcot(x)) is 2(2xcos(x)cot(x)+(-cos(x)-cot(x)csc(x))x^2)

What is the first derivative of 2x^2cos(xcot(x)) ?

The first derivative of 2x^2cos(xcot(x)) is 2(2xcos(x)cot(x)+(-cos(x)-cot(x)csc(x))x^2)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{2}, g = cos (x) cot (x)

= 2 (\frac{d}{d x} (x^{2}) cos (x) cot (x) + \frac{d}{d x} (cos (x) cot (x)) x^{2})

\frac{d}{d x} (x^{2}) = 2 x

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

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

\frac{d y}{d x}, x y - 8 = 0

f (x) = 5 x

\int_{1}^{4} x (1 + x) d x

What is the derivative of 2x^2cos(xcot(x)) ?
The derivative of 2x^2cos(xcot(x)) is 2(2xcos(x)cot(x)+(-cos(x)-cot(x)csc(x))x^2)
What is the first derivative of 2x^2cos(xcot(x)) ?
The first derivative of 2x^2cos(xcot(x)) is 2(2xcos(x)cot(x)+(-cos(x)-cot(x)csc(x))x^2)