What is the tangent of y=4^{x/(ln(2))},\at x=ln(16) ?

The tangent of y=4^{x/(ln(2))},\at x=ln(16) is y=512x+256-2048ln(2)

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tangent of y=4^{x/(ln(2))},\at x=ln(16)

tangent of

y = 4^{\frac{x}{l n ( 2 )}}, at x = ln (16)

y = 512 x + 256 - 2048 ln (2)

Solution steps

Find the tangent point:

(ln (16), 256)

Find the slope of

y = 4^{\frac{x}{l n ( 2 )}} : \frac{d y}{d x} = 2 e^{2 x}

Compute the slope of

y = 4^{\frac{x}{l n ( 2 )}}

x = ln (16) : m = 512

Find the line with slope m=

512

and passing through

(ln (16), 256) : y = 512 x + 256 - 2048 ln (2)

y = 512 x + 256 - 2048 ln (2)

\int \frac{1}{5 x ^{2}} d x

\int_{0}^{l n (7)} x e^{x} d x

x \to 3 lim (\frac{x ^{3} - 1}{x - 1})

sin (π - x)

\frac{\partial ^{2}}{\partial x ^{2}} (ln (3 x + 3 c t))

What is the tangent of y=4^{x/(ln(2))},\at x=ln(16) ?
The tangent of y=4^{x/(ln(2))},\at x=ln(16) is y=512x+256-2048ln(2)