What is the tangent of f(x)=tan(2x),\at x=0 ?

The tangent of f(x)=tan(2x),\at x=0 is y=2x

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tangent of f(x)=tan(2x),\at x=0

tangent of

f (x) = tan (2 x), at x = 0

y = 2 x

Solution steps

Find the tangent point:

(0, 0)

Find the slope of

f (x) = tan (2 x) : \frac{df ( x )}{d x} = sec^{2} (2 x) \cdot 2

Compute the slope of

f (x) = tan (2 x)

x = 0 : m = 2

Find the line with slope m=

2

and passing through

(0, 0) : y = 2 x

y = 2 x

f (x) = x^{5} - 2 x^{3} + x

y = 2 - x^{2}

3 x^{2} - 4

y = x^{2}

y = 5

What is the tangent of f(x)=tan(2x),\at x=0 ?
The tangent of f(x)=tan(2x),\at x=0 is y=2x