What is the derivative of 2sqrt(1+sin(2t)) ?

The derivative of 2sqrt(1+sin(2t)) is (2cos(2t))/(sqrt(1+sin(2t)))

What is the first derivative of 2sqrt(1+sin(2t)) ?

The first derivative of 2sqrt(1+sin(2t)) is (2cos(2t))/(sqrt(1+sin(2t)))

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derivative of

2 1 + sin (2 t)

\frac{2 cos ( 2 t )}{1 + sin ( 2 t )}

Solution steps

\frac{d}{d t} (2 1 + sin (2 t))

Take the constant out:

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

= 2 \frac{d}{d t} (1 + sin (2 t))

Apply the chain rule:

\frac{1}{2 1 + sin ( 2 t )} \frac{d}{d t} (1 + sin (2 t))

= \frac{1}{2 1 + sin ( 2 t )} \frac{d}{d t} (1 + sin (2 t))

\frac{d}{d t} (1 + sin (2 t)) = 2 cos (2 t)

= 2 \cdot \frac{1}{2 1 + sin ( 2 t )} \cdot 2 cos (2 t)

Simplify

2 \cdot \frac{1}{2 1 + sin ( 2 t )} \cdot 2 cos (2 t) : \frac{2 cos ( 2 t )}{1 + sin ( 2 t )}

= \frac{2 cos ( 2 t )}{1 + sin ( 2 t )}

\int (x + 1) 8 x + 9 d x

t a y l or \frac{2 x}{( 1 + x ^{2} ) ^{2}}

l a pl a ce t r an s f or m e^{- t} + 2 e^{- 2 t} + t e^{- 3 t}

\int \frac{5 cosh ( x )}{x} d x

n = 0 \sum \infty \frac{n}{2 n ^{2} + 1}

What is the derivative of 2sqrt(1+sin(2t)) ?
The derivative of 2sqrt(1+sin(2t)) is (2cos(2t))/(sqrt(1+sin(2t)))
What is the first derivative of 2sqrt(1+sin(2t)) ?
The first derivative of 2sqrt(1+sin(2t)) is (2cos(2t))/(sqrt(1+sin(2t)))