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Popular >

derivative of 4xcsc(x)

Solution

\frac{d}{d x} (4 x csc (x))

Solution

4 (csc (x) - x cot (x) csc (x))

Solution steps

\frac{d}{d x} (4 x csc (x))

Take the constant out:

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

= 4 \frac{d}{d x} (x csc (x))

Apply the Product Rule:

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

f = x, g = csc (x)

= 4 (\frac{d x}{d x} csc (x) + \frac{d}{d x} (csc (x)) x)

\frac{d x}{d x} = 1

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

= 4 (1 \cdot csc (x) + (- cot (x) csc (x)) x)

Simplify

= 4 (csc (x) - x cot (x) csc (x))

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 4xcsc(x) ?
The derivative of 4xcsc(x) is 4(csc(x)-xcot(x)csc(x))
What is the first derivative of 4xcsc(x) ?
The first derivative of 4xcsc(x) is 4(csc(x)-xcot(x)csc(x))