What is the tangent of 2x^2+2x ?

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

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tangent of 2x^2+2x

tangent of

2 x^{2} + 2 x

y = (4 a_{0} + 2) 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} + 2 a_{0})

Find the slope of

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

Compute the slope of

y = 2 x^{2} + 2 x

x = a_{0} : m = 4 a_{0} + 2

Find the line with slope m=

4 a_{0} + 2

and passing through

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

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

\int e^{6 x} sin (3 x) d x

\frac{\partial}{\partial x} (x ln (\frac{x}{y ^{2}}))

n \to \infty lim (ln (2))

\frac{d y}{d x} + 4 x y = 8 x^{3}

\frac{d}{d x} (\frac{cos ( x )}{5})

What is the tangent of 2x^2+2x ?
The tangent of 2x^2+2x is y=(4a_{0}+2)x-2a_{0}^2