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}

y^{^{''}} + 9 y = x e^{x}

\int_{1200}^{1201} 0.1

\frac{d}{d x} (- 5 ln (cos (x)))

\int_{- 5}^{5} \frac{1}{v} d v

\int e^{3 x} \cdot e^{3 x} - 4 d x