What is the d/(dt)(6sin(2t)) ?

The d/(dt)(6sin(2t)) is 12cos(2t)

What is the first d/(dt)(6sin(2t)) ?

The first d/(dt)(6sin(2t)) is 12cos(2t)

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\frac{d}{d t} (6 sin (2 t))

12 cos (2 t)

Solution steps

\frac{d}{d t} (6 sin (2 t))

Take the constant out:

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

= 6 \frac{d}{d t} (sin (2 t))

Apply the chain rule:

cos (2 t) \frac{d}{d t} (2 t)

= cos (2 t) \frac{d}{d t} (2 t)

\frac{d}{d t} (2 t) = 2

= 6 cos (2 t) \cdot 2

Simplify

= 12 cos (2 t)

\int_{- \infty}^{- 1} e^{- 10 t} d t

\int_{1}^{\infty} x^{- \frac{7}{4}} d x

\frac{d}{d x} (- \frac{3 x ^{2}}{2 y})

\frac{1}{x ^{2} + x + 1}

x \to 3 lim (5 x^{3} - 3 x^{2} + x - 6)