What is the tangent of (x^2-3x+3)sqrt(25-x^2) ?

The tangent of (x^2-3x+3)sqrt(25-x^2) is

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tangent of (x^2-3x+3)sqrt(25-x^2)

tangent of

(x^{2} - 3 x + 3) 25 - x^{2}

y = \frac{- 3 a _{0}^{3} + 6 a _{0}^{2} + 47 a _{0} - 75}{25 - a _{0}^{2}} x + (a_{0}^{2} - 3 a_{0} + 3) 25 - a_{0}^{2} - \frac{a _{0} ( - 3 a _{0}^{3} + 6 a _{0}^{2} + 47 a _{0} - 75 )}{25 - 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} - 3 a_{0} + 3) 25 - a_{0}^{2})

Find the slope of

y = (x^{2} - 3 x + 3) 25 - x^{2} : \frac{d y}{d x} = \frac{- 3 x ^{3} + 6 x ^{2} + 47 x - 75}{25 - x ^{2}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = \frac{- 3 a _{0}^{3} + 6 a _{0}^{2} + 47 a _{0} - 75}{25 - a _{0}^{2}}

Find the line with slope m=

\frac{- 3 a _{0}^{3} + 6 a _{0}^{2} + 47 a _{0} - 75}{25 - a _{0}^{2}}

and passing through

(a_{0}, (a_{0}^{2} - 3 a_{0} + 3) 25 - a_{0}^{2}) : y = \frac{- 3 a _{0}^{3} + 6 a _{0}^{2} + 47 a _{0} - 75}{25 - a _{0}^{2}} x + (a_{0}^{2} - 3 a_{0} + 3) 25 - a_{0}^{2} - \frac{a _{0} ( - 3 a _{0}^{3} + 6 a _{0}^{2} + 47 a _{0} - 75 )}{25 - a _{0}^{2}}

y = \frac{- 3 a _{0}^{3} + 6 a _{0}^{2} + 47 a _{0} - 75}{25 - a _{0}^{2}} x + (a_{0}^{2} - 3 a_{0} + 3) 25 - a_{0}^{2} - \frac{a _{0} ( - 3 a _{0}^{3} + 6 a _{0}^{2} + 47 a _{0} - 75 )}{25 - a _{0}^{2}}

\int \frac{x ^{2}}{x + 8} d x

\int \frac{1}{x 3 x} d x

\int_{1}^{8} \frac{x}{x ^{2} + 4 x + 13} d x

f (x) = 2 - 2 x

f^{^{''}} (x) = x^{2}, f^{^{'}} (0) = 6, f (0) = 3

What is the tangent of (x^2-3x+3)sqrt(25-x^2) ?
The tangent of (x^2-3x+3)sqrt(25-x^2) is