What is derivative of y(X)= 1/(2cos^2(X)) ?

The answer to derivative of y(X)= 1/(2cos^2(X)) is (dy}{dx}=\frac{sec^3(x)sin(x)-y)/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of y(X)= 1/(2cos^2(X))

derivative of

y = \frac{1}{2 cos ^{2} ( x )}

\frac{d y}{d x} = \frac{sec ^{3} ( x ) sin ( x ) - y}{x}

Solution steps

y x = \frac{1}{2 cos ^{2} ( x )}

Treat

y

y (x)

Differentiate both sides:

x \frac{d y}{d x} + y = sec^{3} (x) sin (x)

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{sec ^{3} ( x ) sin ( x ) - y}{x}

\frac{d y}{d x} = \frac{sec ^{3} ( x ) sin ( x ) - y}{x}

What is derivative of y(X)= 1/(2cos^2(X)) ?
The answer to derivative of y(X)= 1/(2cos^2(X)) is (dy}{dx}=\frac{sec^3(x)sin(x)-y)/x