What is the derivative of e^{cos(2x}*sin(2x)) ?

The derivative of e^{cos(2x}*sin(2x)) is -2e^{cos(2x)}sin^2(2x)+2e^{cos(2x)}cos(2x)

What is the first derivative of e^{cos(2x}*sin(2x)) ?

The first derivative of e^{cos(2x}*sin(2x)) is -2e^{cos(2x)}sin^2(2x)+2e^{cos(2x)}cos(2x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (e^{c o s (2 x)} \cdot sin (2 x))

- 2 e^{c o s (2 x)} sin^{2} (2 x) + 2 e^{c o s (2 x)} cos (2 x)

Solution steps

\frac{d}{d x} (e^{c o s (2 x)} sin (2 x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{c o s (2 x)}, g = sin (2 x)

= \frac{d}{d x} (e^{c o s (2 x)}) sin (2 x) + \frac{d}{d x} (sin (2 x)) e^{c o s (2 x)}

\frac{d}{d x} (e^{c o s (2 x)}) = - 2 e^{c o s (2 x)} sin (2 x)

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

= (- 2 e^{c o s (2 x)} sin (2 x)) sin (2 x) + cos (2 x) \cdot 2 e^{c o s (2 x)}

Simplify

(- 2 e^{c o s (2 x)} sin (2 x)) sin (2 x) + cos (2 x) \cdot 2 e^{c o s (2 x)} : - 2 e^{c o s (2 x)} sin^{2} (2 x) + 2 e^{c o s (2 x)} cos (2 x)

= - 2 e^{c o s (2 x)} sin^{2} (2 x) + 2 e^{c o s (2 x)} cos (2 x)

x \to \infty lim (xxxxx)

\frac{\partial}{\partial x} (\frac{1}{2} x)

ln (3) x^{4}

x^{\frac{2}{3}} (x - 5)

f (x) = \frac{ln ( 15 - 23 x ^{2} )}{8 x ^{5}}

What is the derivative of e^{cos(2x}*sin(2x)) ?
The derivative of e^{cos(2x}*sin(2x)) is -2e^{cos(2x)}sin^2(2x)+2e^{cos(2x)}cos(2x)
What is the first derivative of e^{cos(2x}*sin(2x)) ?
The first derivative of e^{cos(2x}*sin(2x)) is -2e^{cos(2x)}sin^2(2x)+2e^{cos(2x)}cos(2x)