What is the tangent of f(x)=x^7 ?

The tangent of f(x)=x^7 is y=7a_{0}^6x-6a_{0}^7

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tangent of f(x)=x^7

tangent of

f (x) = x^{7}

y = 7 a_{0}^{6} x - 6 a_{0}^{7}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{7})

Find the slope of

f (x) = x^{7} : \frac{df ( x )}{d x} = 7 x^{6}

Compute the slope of

f (x) = x^{7}

x = a_{0} : m = 7 a_{0}^{6}

Find the line with slope m=

7 a_{0}^{6}

and passing through

(a_{0}, a_{0}^{7}) : y = 7 a_{0}^{6} x - 6 a_{0}^{7}

y = 7 a_{0}^{6} x - 6 a_{0}^{7}

2 t sin (t)

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

f (x) = x, at x = \frac{1}{9}

\frac{d}{d x} (sin (2 x))

\frac{\partial}{\partial x} (5 x^{\frac{4}{5}} y^{\frac{1}{5}})

What is the tangent of f(x)=x^7 ?
The tangent of f(x)=x^7 is y=7a_{0}^6x-6a_{0}^7