What is the derivative of f(x)=5xe^xcsc(x) ?

The derivative of f(x)=5xe^xcsc(x) is 5(e^xcsc(x)+x(e^xcsc(x)-e^xcot(x)csc(x)))

What is the first derivative of f(x)=5xe^xcsc(x) ?

The first derivative of f(x)=5xe^xcsc(x) is 5(e^xcsc(x)+x(e^xcsc(x)-e^xcot(x)csc(x)))

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derivative of

f (x) = 5 x e^{x} csc (x)

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

Solution steps

\frac{d}{d x} (5 x e^{x} csc (x))

Take the constant out:

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

= 5 \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)

= 5 (\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)

= 5 (1 \cdot e^{x} csc (x) + (e^{x} csc (x) - e^{x} cot (x) csc (x)) x)

Simplify

= 5 (e^{x} csc (x) + x (e^{x} csc (x) - e^{x} cot (x) csc (x)))

\frac{d}{d x} (7 + 5 x - 5 x^{3} + \frac{7}{x ^{3}})

x \to 0 lim (- x^{2})

t \to - 5 lim (\frac{t ^{2}}{5 - t})

\int 13 - 4 x^{2} d x

d y = cos (x - y) d x

What is the derivative of f(x)=5xe^xcsc(x) ?
The derivative of f(x)=5xe^xcsc(x) is 5(e^xcsc(x)+x(e^xcsc(x)-e^xcot(x)csc(x)))
What is the first derivative of f(x)=5xe^xcsc(x) ?
The first derivative of f(x)=5xe^xcsc(x) is 5(e^xcsc(x)+x(e^xcsc(x)-e^xcot(x)csc(x)))