What is the derivative of e^{sqrt(1+sin(2x)}) ?

The derivative of e^{sqrt(1+sin(2x)}) is (e^{sqrt(1+sin(2x))}cos(2x))/(sqrt(1+sin(2x)))

What is the first derivative of e^{sqrt(1+sin(2x)}) ?

The first derivative of e^{sqrt(1+sin(2x)}) is (e^{sqrt(1+sin(2x))}cos(2x))/(sqrt(1+sin(2x)))

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\frac{d}{d x} (e^{1 + s i n (2 x)})

\frac{e ^{1 + s i n (2 x)} cos ( 2 x )}{1 + sin ( 2 x )}

Solution steps

\frac{d}{d x} (e^{1 + s i n (2 x)})

Apply the chain rule:

e^{1 + s i n (2 x)} \frac{d}{d x} (1 + sin (2 x))

= e^{1 + s i n (2 x)} \frac{d}{d x} (1 + sin (2 x))

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

= e^{1 + s i n (2 x)} \frac{cos ( 2 x )}{1 + sin ( 2 x )}

Multiply fractions:

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

= \frac{e ^{1 + s i n (2 x)} cos ( 2 x )}{1 + sin ( 2 x )}

tan (x), - \frac{π}{4}

x^{3} y^{^{'}} + x y = 1

n = 1 \sum \infty \frac{2 + n}{1 - 2 n}

\int 2 e^{\frac{x}{3}} d x

sin (5 t) e^{(- 2 t)}

What is the derivative of e^{sqrt(1+sin(2x)}) ?
The derivative of e^{sqrt(1+sin(2x)}) is (e^{sqrt(1+sin(2x))}cos(2x))/(sqrt(1+sin(2x)))
What is the first derivative of e^{sqrt(1+sin(2x)}) ?
The first derivative of e^{sqrt(1+sin(2x)}) is (e^{sqrt(1+sin(2x))}cos(2x))/(sqrt(1+sin(2x)))