What is the tangent of 2x^2 ?

The tangent of 2x^2 is y=4a_{0}x-2a_{0}^2

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tangent of 2x^2

tangent of

2 x^{2}

y = 4 a_{0} x - 2 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = 2 x^{2} : \frac{d y}{d x} = 4 x

Compute the slope of

y = 2 x^{2}

x = a_{0} : m = 4 a_{0}

Find the line with slope m=

4 a_{0}

and passing through

(a_{0}, 2 a_{0}^{2}) : y = 4 a_{0} x - 2 a_{0}^{2}

y = 4 a_{0} x - 2 a_{0}^{2}

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

1 + x^{2}

\frac{d y}{d x} = e^{2 x} (1 + y^{2})

y = 3 x^{2} + 5

\int \frac{2}{5 cos ^{2} ( x )} d x