What is the tangent of 1/2 x^4-8 ?

The tangent of 1/2 x^4-8 is y=2a_{0}^3x-3/2 a_{0}^4-8

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tangent of 1/2 x^4-8

tangent of

\frac{1}{2} x^{4} - 8

y = 2 a_{0}^{3} x - \frac{3}{2} a_{0}^{4} - 8

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{1}{2} a_{0}^{4} - 8)

Find the slope of

y = \frac{1}{2} x^{4} - 8 : \frac{d y}{d x} = 2 x^{3}

Compute the slope of

y = \frac{1}{2} x^{4} - 8

x = a_{0} : m = 2 a_{0}^{3}

Find the line with slope m=

2 a_{0}^{3}

and passing through

(a_{0}, \frac{1}{2} a_{0}^{4} - 8) : y = 2 a_{0}^{3} x - \frac{3}{2} a_{0}^{4} - 8

y = 2 a_{0}^{3} x - \frac{3}{2} a_{0}^{4} - 8

x y \frac{d y}{d x} + 4 x^{2} + y^{2} = 0

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

x = y^{2} - 4 y, x = 2 y - y^{2}

\int \frac{1}{t ^{2} 400 - t ^{2}} d t

\frac{d}{d x} (cos (arctan (3 x)))

What is the tangent of 1/2 x^4-8 ?
The tangent of 1/2 x^4-8 is y=2a_{0}^3x-3/2 a_{0}^4-8