What is the derivative of cos(x^2(2x)) ?

The derivative of cos(x^2(2x)) is 2(-2x^2sin(x^2)+cos(x^2))

What is the first derivative of cos(x^2(2x)) ?

The first derivative of cos(x^2(2x)) is 2(-2x^2sin(x^2)+cos(x^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (cos (x^{2}) (2 x))

2 (- 2 x^{2} sin (x^{2}) + cos (x^{2}))

Solution steps

\frac{d}{d x} (cos (x^{2}) (2 x))

Take the constant out:

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

= 2 \frac{d}{d x} (cos (x^{2}) x)

Apply the Product Rule:

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

f = cos (x^{2}), g = x

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

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

\frac{d x}{d x} = 1

= 2 ((- sin (x^{2}) \cdot 2 x) x + 1 \cdot cos (x^{2}))

Simplify

2 ((- sin (x^{2}) \cdot 2 x) x + 1 \cdot cos (x^{2})) : 2 (- 2 x^{2} sin (x^{2}) + cos (x^{2}))

= 2 (- 2 x^{2} sin (x^{2}) + cos (x^{2}))

5 x^{2} - 3 x + 1

\frac{d}{d x} (3 \cdot 5^{x})

x \to 3 lim (2 x^{3} - 10 x - 8)

x \to 0 lim (\frac{x ^{2} - 9}{x - 3})

x \to 0 lim (\frac{( 3 + x ) ^{2} - 9}{x})

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