What is the tangent of e^x,\at x=5 ?

The tangent of e^x,\at x=5 is y=e^5x-4e^5

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tangent of e^x,\at x=5

tangent of

e^{x}, at x = 5

y = e^{5} x - 4 e^{5}

Solution steps

Find the tangent point:

(5, e^{5})

Find the slope of

y = e^{x} : \frac{d y}{d x} = e^{x}

Compute the slope of

y = e^{x}

x = 5 : m = e^{5}

Find the line with slope m=

e^{5}

and passing through

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

y = e^{5} x - 4 e^{5}

\frac{d}{d x} (x^{5} sin (x) tan (x))

x \to - 5 - lim (\frac{8}{( - 5 ) + 5})

\frac{d}{d x} ((3 x - 1)^{5})

\int \frac{1}{x ^{2} y} d y

- x^{3} + 9 x^{2} - 6 x + 9