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#