What is the tangent of f(x)=5e^x,\at x=3 ?

The tangent of f(x)=5e^x,\at x=3 is y=5e^3x-10e^3

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tangent of f(x)=5e^x,\at x=3

tangent of

f (x) = 5 e^{x}, at x = 3

y = 5 e^{3} x - 10 e^{3}

Solution steps

Find the tangent point:

(3, 5 e^{3})

Find the slope of

f (x) = 5 e^{x} : \frac{df ( x )}{d x} = 5 e^{x}

Compute the slope of

f (x) = 5 e^{x}

x = 3 : m = 5 e^{3}

Find the line with slope m=

5 e^{3}

and passing through

(3, 5 e^{3}) : y = 5 e^{3} x - 10 e^{3}

y = 5 e^{3} x - 10 e^{3}

\frac{d y}{d x} = \frac{sin ( 2 x )}{e ^{y}}

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

\int 36 (4 x + 4)^{(2)} - 2 (3 x - 1) d x

\int cos^{- 1} (x) d x

x^{2} + 9

What is the tangent of f(x)=5e^x,\at x=3 ?
The tangent of f(x)=5e^x,\at x=3 is y=5e^3x-10e^3