What is the derivative of 1/3 sin^3(x-sin(x)+1) ?

The derivative of 1/3 sin^3(x-sin(x)+1) is -cos^3(x)

What is the first derivative of 1/3 sin^3(x-sin(x)+1) ?

The first derivative of 1/3 sin^3(x-sin(x)+1) is -cos^3(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (\frac{1}{3} sin^{3} (x) - sin (x) + 1)

- cos^{3} (x)

Solution steps

\frac{d}{d x} (\frac{1}{3} sin^{3} (x) - sin (x) + 1)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{1}{3} sin^{3} (x)) - \frac{d}{d x} (sin (x)) + \frac{d}{d x} (1)

\frac{d}{d x} (\frac{1}{3} sin^{3} (x)) = sin^{2} (x) cos (x)

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

\frac{d}{d x} (1) = 0

= sin^{2} (x) cos (x) - cos (x) + 0

Simplify

sin^{2} (x) cos (x) - cos (x) + 0 : - cos^{3} (x)

= - cos^{3} (x)

x \to 4 lim (\frac{x + 4}{x + 7})

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

t a y l or arctan (2 x)

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

\int 9 - 4 x d x

What is the derivative of 1/3 sin^3(x-sin(x)+1) ?
The derivative of 1/3 sin^3(x-sin(x)+1) is -cos^3(x)
What is the first derivative of 1/3 sin^3(x-sin(x)+1) ?
The first derivative of 1/3 sin^3(x-sin(x)+1) is -cos^3(x)