What is the tangent of 30sqrt(x)-3x ?

The tangent of 30sqrt(x)-3x is y=((15)/(sqrt(a_{0))}-3)x+15sqrt(a_{0)}

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tangent of 30sqrt(x)-3x

tangent of

30 x - 3 x

y = (\frac{15}{a _{0}} - 3) x + 15 a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 30 a_{0} - 3 a_{0})

Find the slope of

y = 30 x - 3 x : \frac{d y}{d x} = \frac{15}{x} - 3

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{15}{a _{0}} - 3

Find the line with slope m=

\frac{15}{a _{0}} - 3

and passing through

(a_{0}, 30 a_{0} - 3 a_{0}) : y = (\frac{15}{a _{0}} - 3) x + 15 a_{0}

y = (\frac{15}{a _{0}} - 3) x + 15 a_{0}

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

\frac{d}{d x} (x^{4} (tan (x) + sec (x)))

x \to 0 lim (- x^{2} + 5 x + a)

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

\frac{d}{d t} (t^{2} (3 - t)^{3})

What is the tangent of 30sqrt(x)-3x ?
The tangent of 30sqrt(x)-3x is y=((15)/(sqrt(a_{0))}-3)x+15sqrt(a_{0)}