What is the tangent of f(x)= x/((5x-4)^8),\at x=1 ?

The tangent of f(x)= x/((5x-4)^8),\at x=1 is y=-39x+40

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tangent of f(x)= x/((5x-4)^8),\at x=1

tangent of

f (x) = \frac{x}{( 5 x - 4 ) ^{8}}, at x = 1

y = - 39 x + 40

Solution steps

Find the tangent point:

(1, 1)

Find the slope of

f (x) = \frac{x}{( 5 x - 4 ) ^{8}} : \frac{df ( x )}{d x} = \frac{- 4 - 35 x}{( 5 x - 4 ) ^{9}}

Compute the slope of

f (x) = \frac{x}{( 5 x - 4 ) ^{8}}

x = 1 : m = - 39

Find the line with slope m=

- 39

and passing through

(1, 1) : y = - 39 x + 40

y = - 39 x + 40

(- 2.2) (5.3)

y = x (x + 1)^{5}, (1, 32)

\int_{\frac{3}{4}}^{1} 2 x d x

\frac{d y}{d x} + y^{9} x + 6 y = 0

y^{^{''}} + 2 y^{^{'}} + y = e - t ln (t)

What is the tangent of f(x)= x/((5x-4)^8),\at x=1 ?
The tangent of f(x)= x/((5x-4)^8),\at x=1 is y=-39x+40