What is the tangent of x^5 ?

The tangent of x^5 is y=5a_{0}^4x-4a_{0}^5

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tangent of x^5

tangent of

x^{5}

y = 5 a_{0}^{4} x - 4 a_{0}^{5}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{5})

Find the slope of

y = x^{5} : \frac{d y}{d x} = 5 x^{4}

Compute the slope of

y = x^{5}

x = a_{0} : m = 5 a_{0}^{4}

Find the line with slope m=

5 a_{0}^{4}

and passing through

(a_{0}, a_{0}^{5}) : y = 5 a_{0}^{4} x - 4 a_{0}^{5}

y = 5 a_{0}^{4} x - 4 a_{0}^{5}

\int csc^{2} (\frac{x}{3}) d x

\frac{\partial}{\partial y} (5 y^{2} e^{5 x y})

\int sin (wt) d t

x y^{^{'}} = \frac{1}{y ^{3}}

\int_{- 1}^{2} (- x^{2} + x + 2)^{2} d x