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

1 Answer
Apr 14, 2015

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