What is the derivative of 8xcos(x^2) ?

The derivative of 8xcos(x^2) is 8(cos(x^2)-2x^2sin(x^2))

What is the first derivative of 8xcos(x^2) ?

The first derivative of 8xcos(x^2) is 8(cos(x^2)-2x^2sin(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} (8 x cos (x^{2}))

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

Solution steps

\frac{d}{d x} (8 x cos (x^{2}))

Take the constant out:

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

= 8 \frac{d}{d x} (x cos (x^{2}))

Apply the Product Rule:

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

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

= 8 (\frac{d x}{d x} cos (x^{2}) + \frac{d}{d x} (cos (x^{2})) x)

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

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

= 8 (1 \cdot cos (x^{2}) + (- sin (x^{2}) \cdot 2 x) x)

Simplify

8 (1 \cdot cos (x^{2}) + (- sin (x^{2}) \cdot 2 x) x) : 8 (cos (x^{2}) - 2 x^{2} sin (x^{2}))

= 8 (cos (x^{2}) - 2 x^{2} sin (x^{2}))

x \to 8 lim ({f (7) g (- 7)})

\int \frac{4 x ^{2} + 8}{2 x ^{2} + 1} d x

\int \frac{1}{x 25 x ^{2} - 4} d x

\int \frac{e ^{y}}{1 - e ^{y}} d y

x \to 0 lim (\frac{0 x ^{4} + e ^{0 x}}{x ^{4}})

What is the derivative of 8xcos(x^2) ?
The derivative of 8xcos(x^2) is 8(cos(x^2)-2x^2sin(x^2))
What is the first derivative of 8xcos(x^2) ?
The first derivative of 8xcos(x^2) is 8(cos(x^2)-2x^2sin(x^2))