What is the tangent of y=e^{4x} ?

The tangent of y=e^{4x} is y=e^{4a_{0}}*4x+e^{4a_{0}}-e^{4a_{0}}*4a_{0}

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tangent of y=e^{4x}

tangent of

y = e^{4 x}

y = e^{4 a_{0}} \cdot 4 x + e^{4 a_{0}} - e^{4 a_{0}} \cdot 4 a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, e^{4 a_{0}})

Find the slope of

y = e^{4 x} : \frac{d y}{d x} = e^{4 x} \cdot 4

Compute the slope of

y = e^{4 x}

x = a_{0} : m = e^{4 a_{0}} \cdot 4

Find the line with slope m=

e^{4 a_{0}} 4

and passing through

(a_{0}, e^{4 a_{0}}) : y = e^{4 a_{0}} \cdot 4 x + e^{4 a_{0}} - e^{4 a_{0}} \cdot 4 a_{0}

y = e^{4 a_{0}} \cdot 4 x + e^{4 a_{0}} - e^{4 a_{0}} \cdot 4 a_{0}

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\frac{x ^{2}}{x - 1}

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\int cos^{3} (5 x) d x

What is the tangent of y=e^{4x} ?
The tangent of y=e^{4x} is y=e^{4a_{0}}*4x+e^{4a_{0}}-e^{4a_{0}}*4a_{0}