What is the derivative of 6sin^2(t) ?

The derivative of 6sin^2(t) is 6sin(2t)

What is the first derivative of 6sin^2(t) ?

The first derivative of 6sin^2(t) is 6sin(2t)

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derivative of

6 sin^{2} (t)

6 sin (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:

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

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

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

= 6 \cdot 2 sin (t) cos (t)

Simplify

6 \cdot 2 sin (t) cos (t) : 6 sin (2 t)

= 6 sin (2 t)

What is the derivative of 6sin^2(t) ?
The derivative of 6sin^2(t) is 6sin(2t)
What is the first derivative of 6sin^2(t) ?
The first derivative of 6sin^2(t) is 6sin(2t)