What is the derivative of f(t)=te^tcot(t) ?

The derivative of f(t)=te^tcot(t) is e^tcot(t)+t(e^tcot(t)-e^tcsc^2(t))

What is the first derivative of f(t)=te^tcot(t) ?

The first derivative of f(t)=te^tcot(t) is e^tcot(t)+t(e^tcot(t)-e^tcsc^2(t))

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derivative of

f (t) = t e^{t} cot (t)

e^{t} cot (t) + t (e^{t} cot (t) - e^{t} csc^{2} (t))

Solution steps

\frac{d}{d t} (t e^{t} cot (t))

Apply the Product Rule:

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

f = t, g = e^{t} cot (t)

= \frac{d t}{d t} e^{t} cot (t) + \frac{d}{d t} (e^{t} cot (t)) t

\frac{d t}{d t} = 1

\frac{d}{d t} (e^{t} cot (t)) = e^{t} cot (t) - e^{t} csc^{2} (t)

= 1 \cdot e^{t} cot (t) + (e^{t} cot (t) - e^{t} csc^{2} (t)) t

Simplify

= e^{t} cot (t) + t (e^{t} cot (t) - e^{t} csc^{2} (t))

f (x) = \frac{5}{x}, x = - 1

arctan (\frac{1 - x}{1 + x})

x \to - \infty lim (81 x^{2} + x - 9 x)

n = 0 \sum \infty 9 (\frac{x}{7})^{n}

\frac{d}{d x} (x - 8 x)

What is the derivative of f(t)=te^tcot(t) ?
The derivative of f(t)=te^tcot(t) is e^tcot(t)+t(e^tcot(t)-e^tcsc^2(t))
What is the first derivative of f(t)=te^tcot(t) ?
The first derivative of f(t)=te^tcot(t) is e^tcot(t)+t(e^tcot(t)-e^tcsc^2(t))