What is the derivative of the exponential function $y = e^(4tansqrtx)$ ?

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Answer 1 · 2015-04-14T16:04:23

$dy/dx=(2e^(4tansqrtx)sec^2sqrtx)/sqrtx$

Solution

$y=e^(4tansqrtx)$

Differentiating both sides with respect to 'x'

$dy/dx=d/dx(e^(4tansqrtx))$

$dy/dx=e^(4tansqrtx)d/dx(4tansqrtx)$

$dy/dx=e^(4tansqrtx).4sec^2sqrtx.d/dx(sqrtx)$

$dy/dx=4e^(4tansqrtx)sec^2sqrtx(1/2x^(1/2-1))$

$dy/dx=4/2e^(4tansqrtx)sec^2sqrtx(x^((1-2)/2))$

$dy/dx=2e^(4tansqrtx)sec^2sqrtx(x^((-1)/2))$

$dy/dx=(2e^(4tansqrtx)sec^2sqrtx)/(x^((1)/2))$

$dy/dx=(2e^(4tansqrtx)sec^2sqrtx)/sqrtx$

What is the derivative of the exponential function y = e^(4tansqrtx)y = e^(4tansqrtx)?