What is the tangent of 5x-4sqrt(x) ?

The tangent of 5x-4sqrt(x) is y=(5-2/(sqrt(a_{0))})x-2sqrt(a_{0)}

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tangent of 5x-4sqrt(x)

tangent of

5 x - 4 x

y = (5 - \frac{2}{a _{0}}) x - 2 a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 5 a_{0} - 4 a_{0})

Find the slope of

y = 5 x - 4 x : \frac{d y}{d x} = 5 - \frac{2}{x}

Compute the slope of

y = 5 x - 4 x

x = a_{0} : m = 5 - \frac{2}{a _{0}}

Find the line with slope m=

5 - \frac{2}{a _{0}}

and passing through

(a_{0}, 5 a_{0} - 4 a_{0}) : y = (5 - \frac{2}{a _{0}}) x - 2 a_{0}

y = (5 - \frac{2}{a _{0}}) x - 2 a_{0}

\int 9 tan^{2} (x) sec (x) d x

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\int \frac{e ^{6 x}}{e ^{6 x} + 7} d x

\int \frac{2 x ^{2}}{20 - 5 x ^{3}} d x

x + \frac{1}{x}

What is the tangent of 5x-4sqrt(x) ?
The tangent of 5x-4sqrt(x) is y=(5-2/(sqrt(a_{0))})x-2sqrt(a_{0)}