What is the tangent of f(x)=cos(2x) ?

The tangent of f(x)=cos(2x) is y=-sin(2a_{0})*2x+cos(2a_{0})+2a_{0}sin(2a_{0})

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tangent of f(x)=cos(2x)

tangent of

f (x) = cos (2 x)

y = - sin (2 a_{0}) \cdot 2 x + cos (2 a_{0}) + 2 a_{0} sin (2 a_{0})

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, cos (2 a_{0}))

Find the slope of

f (x) = cos (2 x) : \frac{df ( x )}{d x} = - sin (2 x) \cdot 2

Compute the slope of

f (x) = cos (2 x)

x = a_{0} : m = - sin (2 a_{0}) \cdot 2

Find the line with slope m=

- sin (2 a_{0}) 2

and passing through

(a_{0}, cos (2 a_{0})) : y = - sin (2 a_{0}) \cdot 2 x + cos (2 a_{0}) + 2 a_{0} sin (2 a_{0})

y = - sin (2 a_{0}) \cdot 2 x + cos (2 a_{0}) + 2 a_{0} sin (2 a_{0})

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

\int sec^{5} (x) tan^{3} (x) d x

x \to 0 lim (\frac{( x + 1 ) ^{5} - 1}{x})

\int A \cdot e^{t (1 + 3)} d t

\int \frac{1}{( u - 1 ) ^{2}} d u

What is the tangent of f(x)=cos(2x) ?
The tangent of f(x)=cos(2x) is y=-sin(2a_{0})*2x+cos(2a_{0})+2a_{0}sin(2a_{0})