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

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

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

The first derivative of y=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 >

derivative of

y = cos (x^{2}) \cdot 2 x

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

Solution steps

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

\int 10 x d x

f (x) = - 3 e^{x^{2} + x - 1}

x^{2} y^{^{'}} + 2 x y = ln (x), y (1) = 7

y = 4 + x

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 16 y = 0

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