What is the derivative of 6cos(x)csc(x^2) ?

The derivative of 6cos(x)csc(x^2) is 6(-sin(x)csc(x^2)-2xcot(x^2)csc(x^2)cos(x))

What is the first derivative of 6cos(x)csc(x^2) ?

The first derivative of 6cos(x)csc(x^2) is 6(-sin(x)csc(x^2)-2xcot(x^2)csc(x^2)cos(x))

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derivative of

6 cos (x) csc (x^{2})

6 (- sin (x) csc (x^{2}) - 2 x cot (x^{2}) csc (x^{2}) cos (x))

Solution steps

\frac{d}{d x} (6 cos (x) csc (x^{2}))

Take the constant out:

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

= 6 \frac{d}{d x} (cos (x) csc (x^{2}))

Apply the Product Rule:

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

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

= 6 (\frac{d}{d x} (cos (x)) csc (x^{2}) + \frac{d}{d x} (csc (x^{2})) cos (x))

\frac{d}{d x} (cos (x)) = - sin (x)

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

= 6 ((- sin (x)) csc (x^{2}) + (- cot (x^{2}) csc (x^{2}) \cdot 2 x) cos (x))

Simplify

= 6 (- sin (x) csc (x^{2}) - 2 x cot (x^{2}) csc (x^{2}) cos (x))

What is the derivative of 6cos(x)csc(x^2) ?
The derivative of 6cos(x)csc(x^2) is 6(-sin(x)csc(x^2)-2xcot(x^2)csc(x^2)cos(x))
What is the first derivative of 6cos(x)csc(x^2) ?
The first derivative of 6cos(x)csc(x^2) is 6(-sin(x)csc(x^2)-2xcot(x^2)csc(x^2)cos(x))