Question

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

Answer 1

`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`