What is the derivative of 4xe^xcsc(x) ?

The derivative of 4xe^xcsc(x) is 4(e^xcsc(x)+x(e^xcsc(x)-e^xcot(x)csc(x)))

What is the first derivative of 4xe^xcsc(x) ?

The first derivative of 4xe^xcsc(x) is 4(e^xcsc(x)+x(e^xcsc(x)-e^xcot(x)csc(x)))

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derivative of

4 x e^{x} csc (x)

4 (e^{x} csc (x) + x (e^{x} csc (x) - e^{x} cot (x) csc (x)))

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = e^{x} csc (x)

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

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

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

= 4 (1 \cdot e^{x} csc (x) + (e^{x} csc (x) - e^{x} cot (x) csc (x)) x)

Simplify

= 4 (e^{x} csc (x) + x (e^{x} csc (x) - e^{x} cot (x) csc (x)))

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