What is the derivative of cot(4x^2(x^2-9)) ?

The derivative of cot(4x^2(x^2-9)) is -8xcsc^2(4x^2)(x^2-9)+2xcot(4x^2)

What is the first derivative of cot(4x^2(x^2-9)) ?

The first derivative of cot(4x^2(x^2-9)) is -8xcsc^2(4x^2)(x^2-9)+2xcot(4x^2)

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\frac{d}{d x} (cot (4 x^{2}) (x^{2} - 9))

- 8 x csc^{2} (4 x^{2}) (x^{2} - 9) + 2 x cot (4 x^{2})

Solution steps

\frac{d}{d x} (cot (4 x^{2}) (x^{2} - 9))

Apply the Product Rule:

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

f = cot (4 x^{2}), g = x^{2} - 9

= \frac{d}{d x} (cot (4 x^{2})) (x^{2} - 9) + \frac{d}{d x} (x^{2} - 9) cot (4 x^{2})

\frac{d}{d x} (cot (4 x^{2})) = - csc^{2} (4 x^{2}) \cdot 8 x

\frac{d}{d x} (x^{2} - 9) = 2 x

= (- csc^{2} (4 x^{2}) \cdot 8 x) (x^{2} - 9) + 2 x cot (4 x^{2})

Simplify

= - 8 x csc^{2} (4 x^{2}) (x^{2} - 9) + 2 x cot (4 x^{2})

n = 1 \sum \infty \frac{n + 4}{3 n + 2}

\int \frac{1}{x ^{2} - 4 x} d x

\int \frac{1}{( x ^{2} - 1 ) ^{\frac{1}{2}}} d x

\frac{d y}{d x} = \frac{3}{x y ^{2}}

\int \frac{cos ( 2 ln ( x ) ) ln ( x )}{x} d x

What is the derivative of cot(4x^2(x^2-9)) ?
The derivative of cot(4x^2(x^2-9)) is -8xcsc^2(4x^2)(x^2-9)+2xcot(4x^2)
What is the first derivative of cot(4x^2(x^2-9)) ?
The first derivative of cot(4x^2(x^2-9)) is -8xcsc^2(4x^2)(x^2-9)+2xcot(4x^2)