What is t^{-1}e^{-2t}sin(2t)cosh(t) ?

The solution to t^{-1}e^{-2t}sin(2t)cosh(t) is (sin(2t)cosh(t))/(e^{2t)t}

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simplify t^{-1}e^{-2t}sin(2t)cosh(t)

simplify

t^{- 1} e^{- 2 t} sin (2 t) cosh (t)

\frac{sin ( 2 t ) cosh ( t )}{e ^{2 t} t}

Solution steps

t^{- 1} e^{- 2 t} sin (2 t) cosh (t)

Apply exponent rule:

a^{- 1} = \frac{1}{a}

= e^{- 2 t} \frac{1}{t} sin (2 t) cosh (t)

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{t} \cdot \frac{1}{e ^{2 t}} sin (2 t) cosh (t)

Multiply fractions:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{1 \cdot 1 \cdot sin ( 2 t ) cosh ( t )}{t e ^{2 t}}

Multiply:

1 \cdot 1 \cdot sin (2 t) cosh (t) = sin (2 t) cosh (t)

= \frac{sin ( 2 t ) cosh ( t )}{e ^{2 t} t}

(8 x^{10}) (7 x^{3})

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P^{1} (1, 3, 5) P^{2} (2, - 1, 4)

5 d^{2} e^{4} \cdot 2 e^{6}

(x + 4) (x - 3) (2 x - 1)

What is t^{-1}e^{-2t}sin(2t)cosh(t) ?
The solution to t^{-1}e^{-2t}sin(2t)cosh(t) is (sin(2t)cosh(t))/(e^{2t)t}