What is the tangent of x^2+6x ?

The tangent of x^2+6x is y=(2a_{0}+6)x-a_{0}^2

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tangent of x^2+6x

tangent of

x^{2} + 6 x

y = (2 a_{0} + 6) x - a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{2} + 6 a_{0})

Find the slope of

y = x^{2} + 6 x : \frac{d y}{d x} = 2 x + 6

Compute the slope of

y = x^{2} + 6 x

x = a_{0} : m = 2 a_{0} + 6

Find the line with slope m=

2 a_{0} + 6

and passing through

(a_{0}, a_{0}^{2} + 6 a_{0}) : y = (2 a_{0} + 6) x - a_{0}^{2}

y = (2 a_{0} + 6) x - a_{0}^{2}

\frac{d}{d x} (e^{2 x} e^{3 x} e^{4 x})

f^{^{'}} (x) = x - 3 + π x^{2} - 2

x \to 1 lim (5 x^{2} + 2)

y = x + 1, y = 2 - x + 1, y = 1

x^{2} y^{^{'}} + x y = 1, y (1) = 2