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

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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}

y = 4 x ln (x) + (3^{x}) - (x^{3})

\int \frac{1}{( 256 + x ^{2} ) ^{\frac{3}{2}}} d x

x \to 0 lim ((3 x^{2} - 2)^{5})

\int e^{x} ln (x) d x

4 x^{3} + 8 x^{2} + 3 x + 2

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